Stepping motor with a coded pole pattern

ABSTRACT

The present invention relates to a stepping motor with a magnet pole pattern having a predetermined pattern around the circumference of the stepping motor. In one embodiment, the pattern relates to a code having a unique single maximum autocorrelation peak over the period of the code. Example codes include Barker codes, PN codes, Kasami codes, Golomb ruler codes, and other codes. In one embodiment, the rotor and stator have a matching pole pattern. In one embodiment, the drive is arranged to align the poles in an inline configuration, alternatively, the drive may be arranged to align the poles in a diagonal configuration. In a further embodiment, one or more sets of poles are provided on the stator, each set being offset rotationally by a partial pole spacing.

RELATED APPLICATIONS

This Non-provisional Application claims the benefit under 35 USC 119(e)of prior provisional application 61/247,931 titled “Stepping Motor WithCoded Pole Pattern” filed Oct. 1, 2009 by Fullerton et al; thisNon-provisional application is a continuation-in-part of non-provisionalapplication Ser. No. 12/478,911, titled “Magnetically Attachable andDetachable Panel System,” filed Jun. 5, 2009 by Fullerton et al., nowpublished as US2009/0250574-A1, which is a continuation in part ofnon-provisional application Ser. No. 12/476,952 filed Jun. 2, 2009, byFullerton et al., titled “A Field Emission System and Method”, which isa continuation-in-part of Non-provisional application Ser. No.12/322,561, filed Feb. 4, 2009 by Fullerton et al., titled “System andMethod for Producing an Electric Pulse”, which is a continuation-in-partapplication of Non-provisional application Ser. No. 12/358,423, filedJan. 23, 2009 by Fullerton et al., titled “A Field Emission System andMethod”, which is a continuation-in-part application of Non-provisionalapplication Ser. No. 12/123,718, filed May 20, 2008 by Fullerton et al.,titled “A Field Emission System and Method”, which claims the benefitunder 35 USC 119(e) of U.S. Provisional Application Ser. No. 61/123,019,filed Apr. 4, 2008 by Fullerton, titled “A Field Emission System andMethod.” The US Patent Applications and US Patent Publications listedabove are incorporated herein by reference in their entirety.

Further background may be found in U.S. Pat. No. 7,755,462 issued Jul.13, 2010, titled: “Ring magnet structure having a coded magnet pattern,”filed Jun. 5, 2009 by Fullerton et al. and U.S. Pat. No. 7,750,781,issued Jul. 6, 2010, filed Jun. 5, 2009 by Fullerton et al.

The US patent documents and publications listed above are incorporatedherein by reference in their entirety.

FIELD OF THE INVENTION

The present invention pertains generally to the field of magneticmotors, more particularly to stepping motors.

BACKGROUND

Typical stepping motors have a magnetic pole pattern that repeatsmultiple times around the circumference of the rotor or stator. Therepeating pattern gives rise to significant ambiguity in the position ofthe rotor for any given drive signal configuration. The ambiguity istypically solved by synchronization with mechanical stops or electronicposition sensors.

Thus there is a need for stepping motors with positive positiondetermination without requiring synchronization with mechanical stops orelectronic position sensors.

BRIEF DESCRIPTION OF THE INVENTION

The present invention relates to a stepping motor with a magnet polepattern having a non-repetitive pattern around the circumference of thestepping motor. In one embodiment, the pattern relates to a code havinga unique single maximum autocorrelation peak over the period of thecode. Example codes include Barker codes, PN codes, Kasami codes, Golombruler codes, Maximal Length Linear Feedback Shift Register codes, andother codes.

In one embodiment, the code has an autocorrelation function having asingle maximum peak per code modulo and a plurality of off maximum peakvalues wherein said off maximum peak values are less than some fraction,for example, one half, of the maximum peak.

In one embodiment, the code may preferably be greater than apredetermined length, for example four. Ranges indicated herein areintended to include any subrange.

In one embodiment, the rotor and stator have a matching pole pattern.

In one embodiment, the drive is arranged to align the poles in an inlineconfiguration, alternatively, the drive may be arranged to align thepoles in a diagonal configuration.

In a further embodiment, a first set of poles and a second set of polesare provided on the stator such that the first set and the second sethave the same pattern, each pole pattern having a fixed pole to polespacing, the first set and the second set being offset rotationally bypartial pole spacing, preferably a half pole spacing. Additional sets ofpoles may be provided, each separated by a partial pole spacing,alternatively referred to as a partial pole shift in phase.

In a further embodiment, the poles of the stator have the same sequenceas the poles of the rotor, but are offset by an incremental amount perpole to generate a vernier pole pattern.

In a further embodiment, two levels of poles may be provided.Hierarchical pole sets may be provided according to a first code. Eachpole set may comprise a set of poles according to a second code.

In one embodiment, the stepping motor has a single stable lock-in angleper revolution. In another embodiment, more than one code modulo may beused around the rotor and thus there may be more than one stable lock-inpoint per revolution.

In a further embodiment, a composite drive is provided to the stator ofthe stepping motor. The composite drive may be the summation of multipleshifted copies of the rotor code pattern.

The invention further includes associated methods for making and using astepping motor with a coded pole pattern.

These and further benefits and features of the present invention areherein described in detail with reference to exemplary embodiments inaccordance with the invention.

BRIEF DESCRIPTION OF THE FIGURES

The present invention is described with reference to the accompanyingdrawings. In the drawings, like reference numbers indicate identical orfunctionally similar elements. Additionally, the left-most digit(s) of areference number identifies the drawing in which the reference numberfirst appears.

FIG. 1A and FIG. 1B depict an exemplary stepping motor with coded magnetstructures in accordance with the present invention.

FIG. 2A-FIG. 2H illustrate various magnet concepts and structuresutilized by the present invention.

FIG. 3A-FIG. 3N illustrate a sequence of relative shift positions for aBarker 7 magnet structure and a complementary Barker 7 magnet structure.

FIG. 4A and FIG. 4B illustrate the normal force between variably codedmagnet structures for sliding offsets shown in FIGS. 3A-3N.

FIG. 5A and FIG. 5B show the normal force produced by a pair of 7 lengthuniformly coded magnet structures each coded to emulate a single magnet.

FIG. 6A and FIG. 6B show a cyclic implementation of a Barker 7 code.

FIG. 7A and FIG. 7B show two magnet structures coded using a Golombruler code.

FIG. 8A-FIG. 8E show various exemplary two dimensional code structuresin accordance with the present invention.

FIG. 9A-FIG. 9F illustrate additional two dimensional codes derived fromthe single dimension Barker 7 code.

FIG. 9G illustrates a further alternative using four codes of low mutualcross correlation.

FIG. 10A and FIG. 10B depict a magnetic field emission structurecomprising nine magnets in three parallel columns of three magnets eachwith the center column shifted by one half position.

FIG. 11A-FIG. 11C depict an exemplary code intended to produce amagnetic field emission structure having a first stronger lock whenaligned with its mirror image magnetic field emission structure and asecond weaker lock when rotated 90° relative to its mirror imagemagnetic field emission structure.

FIGS. 12A-12I depict the exemplary magnetic field emission structure andits mirror image magnetic field emission structure.

FIG. 13A-FIG. 13D depict various exemplary mechanisms that can be usedwith field emission structures and exemplary tools utilizing fieldemission structures in accordance with the present invention.

FIG. 14A-FIG. 14E illustrate exemplary ring magnet structures based onlinear codes.

FIG. 15A-FIG. 15E depict the components and assembly of an exemplarycovered structural assembly.

FIG. 16A and FIG. 16B illustrate relative force and distancecharacteristics of large magnets as compared with small magnets.

FIG. 16C depicts an exemplary magnetic field emission structure made upof a sparse array of large magnetic sources combined with a large numberof smaller magnetic sources.

FIG. 17A-FIG. 17C illustrate several exemplary cylinder and spherearrangements, some arrangements including coupling with linear trackstructures.

FIG. 18A through FIG. 18H provide a few more examples of how magneticfield sources can be arranged to achieve desirable spatial forcefunction characteristics.

FIG. 19A through FIG. 19G depict exemplary embodiments of twodimensional coded magnet structures.

FIG. 20A and FIG. 20B illustrate a model of the torque generated by thestepping motor of FIG. 1 at full step aligned positions.

FIG. 21A and FIG. 21B illustrate a model of the torque generated by thestepping motor of FIG. 1 at half step positions.

FIG. 22 illustrates the torque patterns for stepping motors as in FIG. 1constructed using various alternative codes.

FIG. 23 illustrates an exemplary composite pattern drive architecture.

FIG. 24 illustrates an exemplary torque vs. position pattern for asingle pattern.

FIG. 25 illustrates an exemplary torque vs. position pattern for acomposite pattern comprising the sum of two single patterns.

FIG. 26-FIG. 33 illustrate exemplary torque vs. position pattern forcomposite patterns comprising various sums of single patterns.

FIG. 34A and FIG. 34B illustrate an exemplary vernier design andillustrates an exemplary compound pole pattern and illustrates anexemplary compound pole pattern applied to a vernier design.

FIG. 35 illustrates various actual torque vs. rotation curves availablewith different pole piece designs.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1A depicts an exemplary single phase stepping motor in accordancewith the present invention. Referring to FIG. 1A, FIG. 1A shows astepping motor 100 having a rotor 108 and stator 106. The rotor andstator each have seven magnets radially magnetized with poles facing oneanother across the rotor/stator gap. A vertical cross section 101 showsthe relative pole orientation of the stator 106 and rotor 108 across therotor/stator gap 107. FIG. 1A shows a stator (outer ring) magnetic polefield pattern 102 and a rotor (inner ring) magnetic field pattern 104.The patterns are shown linearly for simplicity, but actually representthe rotational sequence of magnets in the motor 100. Typically, therotor is permanently magnetized and the stator comprises electromagnetsthat may be driven to generate torque or motion, as desired, in therotor. The stator field pattern is shown using the same code as therotor and in the same position as the rotor, thus, holding the rotor ina stable position. By shifting the stator pattern left or right, torquewill be generated tending to move the rotor to the left or right,respectively. The rotor has a rotational axis 110 shown vertically. Therotor may be operatively coupled to a shaft (not shown). The exemplarypattern 102 shown is for a Barker length 7 code. The inner ringtypically comprises permanent magnets and the outer ring typicallycomprises electromagnets. Other arrangements are possible includingreversal of rotor/stator and electromagnetic and permanent magnetfields. Both may be electromagnetic fields. One or both may beelectro/permanent magnets. The rotor is shown as being configured as acylinder with longitudinal magnets polarized in a radial direction.Alternatively, the rotor may be a disk forming a plane perpendicular tothe rotational axis with radial magnets polarized parallel to the rotoraxis (through the thickness of the disk). In further alternatives, therotor may be a ring (without a shaft). In one embodiment, the ring maydrive a lead screw to provide linear motion. Other arrangements arepossible as are known by those in the art of stepping motors.

The Barker length 7 code is used repeatedly as an example in thisdisclosure. Alternatively Barker codes of other lengths may be used.Also various alternative codes may be used including PN codes, Kasamicodes, Gold codes, Golomb ruler codes and other codes. In oneembodiment, a desirable code property is a single maximumautocorrelation function.

Stepping motors based on codes having a single maximum autocorrelationfunction will have a single stable lock in point, i.e., the rotor andstator will have one particular relative angle where the rotor is heldin place. Other angles will either generate a torque to move toward thestable point or will have nearly zero torque and thus will not lock-into any particular point. These torque profiles will be described laterin this disclosure.

In one embodiment, a code with a desirable cyclic autocorrelationfunction is used to establish the pole configuration for a singlerevolution of the stepping motor such that the beginning and end of thecode are adjacent, utilizing one cycle of the code for one cycle (360degree circle of rotation) of the stepping motor. In an alternativeembodiment, more than one cycle of the code may be used for one 360degree rotation of the stepping motor.

FIG. 1B depicts an exemplary two phase stepping motor in accordance withthe present invention.

FIG. 1B shows the rotor 108 and two stators 106, 120. The two statorshave the same code magnet pattern 102, 112, which matches the pattern ofthe rotor 104. The two stators are offset by one half magnet polespacing width. In operation, the two stators may be driven alternatelyto advance the rotor in a given direction. In one embodiment, a firstrotor is driven with the code pattern. The first rotor may then beturned off and simultaneously, the second rotor is driven with the codepattern to advance the rotor by one half pole distance. Then the secondmay be turned off while simultaneously driving the first with a codepattern advanced by one pole distance from the initial position. Theprocess may then be repeated to advance to a desired position.

Alternatively, the two stators may be driven in an overlapping manner.The two stators are driven simultaneously with code patterns offset byone half pole position. The rotor aligns mid way between the two. Toadvance in a given direction, the stator that lags in the desireddirection is changed to shift the pattern by one pole spacing in thedesired direction. The other stator remains in the same position. Therotor then advances by one half pole spacing in the desired direction.The next move is made by the second stator advancing by one poleposition.

Coded Magnet Structures

Numerous codes of different lengths and geometries are available to suita wide range of applications. A general discussion on codes andgeometries for coded magnet structures will now be described withreference to several drawings.

Coded magnet structures were first fully disclosed in U.S. ProvisionalPatent Application 61/123,019, titled “A Field Emission System andMethod”, filed Apr. 4, 2008. Coded magnet structures are alternativelyreferred to as field emission structures, coded field emissions,correlated magnets, and coded magnets. The fields from coded magnetstructures may be referred to as coded field emissions, correlated fieldemissions, coded magnetic fields, or correlated magnetic fields. Forcesfrom interacting coded magnet structures may be referred to as a spatialforce function or force function resulting from correlated fields.

A coded magnet structure is typically a set of magnets positioned alongan interface boundary with the north-south orientation of eachindividual magnet field at the interface boundary selected to bepositive (north-south) or negative (south-north) according to apredefined pattern, alternatively referred to as a code. Alternatively,the spacing between magnets may be defined by the pattern. The patterntypically appears random or pseudorandom; however, the pattern may becarefully designed or selected to have certain properties desired for agiven application. These properties include, but are not limited toprecise alignment, maximum response at alignment, minimal response outof alignment, the ability to use different codes that prevent alignmentbetween the different codes, but allow alignment for the same code.These properties can be applied to yield a multitude of benefitsincluding but not limited to precise positioning, strong holding force,easy release, unambiguous assembly of multiple parts and/or multiplepositions, rolling contact or contact free power transfer (magneticgears), new types of motors, and magnetic suspension. Note that codedmagnet structures may include contiguous magnet material with a spatialand/or polarity pattern of magnetization along the material. Basic codedmagnet structures will now be introduced with reference to the Figures.

FIG. 2A depicts an exemplary bar magnet showing the South and Northpoles and associated magnetic field vectors. Referring to FIG. 2A, amagnet 200 has a South pole 201 and a North pole 202. Also depicted aremagnetic field vectors 203 that represent the direction and magnitude ofthe magnet's moment. North and South poles are also referred to hereinas positive (+) and negative (−) poles, respectively. In accordance withthe invention, magnets can be permanent magnets, impermanent magnets,electromagnets, involve hard or soft material, and can besuperconductive. In some applications, magnets can be replaced byelectrets. Magnets can be most any size from very large to very small toinclude nanometer scale structures. In the case of non-superconductingmaterials there is a smallest size limit of one domain. When a materialis made superconductive, however, the magnetic field that is within itcan be as complex as desired and there is no practical lower size limituntil you get to atomic scale. Magnets may also be created at atomicscale as electric and magnetic fields produced by molecular sizestructures may be tailored to have correlated properties, e.g.nanomaterials and macromolecules. At the nanometer scale, one or moresingle domains can be used for coding where each single domain has acode and the quantization of the magnetic field would be the domain.

FIG. 2B and FIG. 2C illustrate the familiar magnetic principle thatunlike poles attract and like poles repel. FIG. 2B shows two magnets,magnet 204 and magnet 206 a, arranged to have unlike poles in proximityto one another, the north pole of magnet 204 is near the south pole ofmagnet 206 a, thus the magnetic fields attract and the magnets are drawntogether as shown by the arrows. FIG. 2C shows magnet 204 with magnet206 b arranged with the north poles in proximity. The resulting forcerepels the magnets as shown by the arrows. Coded magnet structuresutilize multiple magnets like those shown in FIG. 2B and FIG. 2C. Amagnet structure typically includes a parallel array of a number ofmagnets oriented N-S interspersed with magnets oriented opposite, orS-N. The magnet structure is typically paired with another magnetstructure of corresponding magnets. The magnets in the correspondingmagnet structure may be selected so that when the two magnet structuresare aligned, each magnet of the first structure is attracted to acorresponding magnet of the second structure. Alternatively the magnetsmay be selected to repel so that when the two magnet structures arealigned, each magnet of the first structure is repelled by acorresponding magnet of the second structure. When the magnet structuresare not aligned, the non-aligned forces combine according to the codeproperties of the particular magnet arrangement. Various codes and theirproperties as applied to magnet arrangement are further discussed inthis disclosure.

FIG. 2D illustrates a linear magnet structure of seven magnets uniformlyoriented in the same direction. The seven magnets bonded together in amagnet structure 212 behave essentially as a single magnet. A magnetstructure typically refers to a set of magnets rigidly bonded togetheras if glued or potted to act mechanically as a single piece, althoughsome flexible bonding arrangements are disclosed. The magnets of themagnet structure 212 depicted in FIG. 2D require bonding since withoutsuch bonding they would naturally orient themselves such that everymagnet would be oriented opposite the orientation of the magnet(s) oneither side of it. Such naturally aligned magnets are not coded magnetstructures, where at least one magnet is oriented in a manner thatrequires a bonding or holding mechanism to maintain its orientation.Each of the seven magnets of FIG. 2D and other illustrations of thisdisclosure may also be referred to as component magnets of the magnetstructure, magnetic field sources, magnetic field emission sources, orfield emission sources.

FIG. 2E illustrates the linear structure of FIG. 2D with the magnets inan exemplary arrangement to form a variably coded structure 214 so thatsome of the magnets have the north pole up and some have the south poleup in accordance with the present invention. Due to the placement ofside by side magnets of the same polarity, the magnets will require aholding force. As such, FIG. 2C depicts a uniformly coded magnetstructure 212 while FIG. 2D depicts a variably coded magnet structure214, where each of the two coded magnet structures requires a bonding orholding mechanism to maintain the orientation of its magnets. As usedherein, a variable code may be a code with both positive and negativepolarities, alternatively as will be discussed later, a variable codemay be a code with different spacings between adjacent magnets.

FIG. 2F shows the top face of the magnet structure of FIG. 2E. Takingthe top face as the reference face 216 of the structure and designating“+” for the north pole and “−” for the south pole, the sequence ofmagnets may be designated “+++−−+−”, as shown. Alternatively, thesequence may be written: “+1, +1, +1, −1, −1, +1, −1”, where “+1”indicates the direction and strength of the magnet as a direction ofnorth and a strength of one unit magnet. For much of the exemplarydiscussion in this disclosure, the actual strength of the magnet isarbitrary. Much of the discussion relates to using several magnets ofequal strength in complex arrangements. Thus, “one magnet” is thearbitrary magnetic strength of a single magnet. Additional coded magnetstructure arrangements for unequal strength or unequal physical sizemagnets may also be developed in accordance with the teachings herein.The surface of the top face 216 may be referred to as an interfacesurface since it can be brought into proximity with a correspondinginterface surface of a second magnet structure in the operation of theinvention to achieve the benefits of the magnet arrangements. Under onearrangement, the surface of the bottom face 217 may also be referred toas a second interface surface 217 since it can be brought into proximitywith a corresponding interface surface of another magnet structure(e.g., a third coded magnet structure) in the operation of the inventionto achieve the benefits of the magnet arrangements. FIG. 2G illustratesthe exemplary magnet structure of FIG. 2E in proximity and in alignmentwith a complementary magnet structure in accordance with the presentinvention. Referring to FIG. 2G, magnet structure 214 has the sequence“+, +, +, −, −, +, −” on interface surface 216. Complementary magnetstructure 220 has the magnetic arrangement sequence: “−, −, −, +, +, −,+” as viewed on the underside surface 217 interfacing with magnetstructure 214. Thus, the sequence is “complementary” as eachcorresponding opposite magnet across the interface plane 216 forms anattraction pair with the magnet of structure 214. A complementary magnetstructure may also refer to a magnet structure where each magnet forms arepelling pair with the corresponding opposite magnet across theinterface plane 214. The interface surface 216 is conformal to aninterface plane 219 dividing the components of structure 214 andcomplementary structure 220 and across which 219 the structures 214 and220 interact. The interface plane 219 may alternatively be referred toas an interface boundary, because the “plane” may take various curved orcomplex shapes including but not limited to the surface of a cylinder,cone, sphere, or stepped flats when applied to various different magnetstructures.

Typically in this disclosure, complementary surfaces of magnetstructures are brought into proximity and alignment to produce anattractive force as the exemplary embodiment. However, the like surfacesof magnet structures can be brought into proximity and alignment toproduce a repelling force, which can be accomplished by rotating one ofthe magnet structures 180° (as indicated by arrow 218) so that two likefaces 217, 217 a (or 216, 216 a) are brought into proximity.Complementary structures are also referred to as being the mirror imageof each other. As described herein, relative alignments between surfacesof magnet structures can be used to produce various combinations ofattraction and repelling forces.

Generally speaking, a given magnet structure is used with acomplementary magnet structure to achieve the desired properties.Typically, complementary structures have the same magnetic fieldmagnitude profile across an interface boundary and may have the same oropposite polarity. Special purpose complementary structures, however,may have differing profiles. Complementary magnet structures may also bereferred to as having a mirror pattern of each other across an interfaceboundary, keeping in mind that the magnets of the structures may haveopposite polarities or the same polarities causing them to attract orrepel each other when aligned, respectively.

FIG. 2H shows an alternate notation illustrating the magnet structures214 and 216 in alignment. The notation of FIG. 2H illustrates the flatside of each magnet with the N-S indication of polarity. Each structure214, 220 is a physically bonded unit, i.e., all magnets of a structuremove right or left, up or down together. The two structures are shown insliding contact at the interface boundary 219 (alternatively referred toas the interface plane 219). (Contact is interesting because forces areat maximum when in contact, but contact is not necessary.) Contactgenerally refers to the condition where the two magnet structures are incontact, whether the magnets themselves are in contact or not. Proximitygenerally means that the two magnet structures are close to one anotherwithin a distance corresponding to a lateral code element spacing, i.e.,magnet to magnet spacing, preferably within half of the code elementspacing. The two structures 214, 220 are free to move relative to eachother and to exert response forces resulting from the interactingmagnetic fields. Alignment of a base structure 214 with a complementarystructure 220 means that each complementary magnet of the complementarystructure is directly across the interface boundary 219 from thecorresponding magnet of the base structure 214. Alignment may also referto alignment of individual magnets, referring then to the alignment ofthe center of the magnetic field with the center of the magnetic fieldof the magnet across the interface surface for maximum attraction orrepelling force. For example, magnet 222 at the right end of the basestructure 214 is aligned with the complementary magnet 224 at the rightend of the complementary structure 220. Magnet 224 is across theinterface boundary 219 from magnet 222. The designation of basestructure and complementary structure is typically a convenience fordiscussion purposes and the terms can be reversed since the twostructures are each complementary structures to each other. Magnets aresubstantially aligned when the magnet axis centers are within a halfwidth of one of the magnets. Magnet structures are substantially alignedwhen the component magnets are substantially aligned. Alternatively,substantial alignment may mean that the magnets or structures are withinhalf of the peak force function from best alignment. Alignment isassumed to include and ignore normal mechanical and other constructiontolerances in practice. Depending on context, especially when discussingmagnet structures of differing codes, alignment may refer to amechanical alignment of the overall structure and/or individual magnetseven though the magnetic fields may not match in a complementary mannerand thus the alignment may not generate a strong attracting or repellingforce.

Magnet structures may be depicted in this disclosure as containingmagnets that entirely fill the space from one position to the next inthe coded structure; however, any or all magnet positions may beoccupied by magnets of lesser width.

The polarity sequence pattern of exemplary magnet structure 214corresponds to the polarity sequence of a 7 length Barker code. Thesequence of the complementary structure 220 corresponds to the reversepolarity of a Barker 7 code. Barker codes have optimal autocorrelationproperties for particular applications, which can result in distinctlyuseful magnetic attraction (or repelling) properties for magnetstructures when applied in accordance with the present invention. Inparticular, one property is to produce a maximum, or peak, attractive orrepelling force when the structures are aligned with greatly reducedforce when misaligned, for example, by one or more magnet widths. Thisproperty can be understood with reference to FIG. 3A-FIG. 3N.

FIG. 3A-FIG. 3N illustrate a sequence of relative shift positions for aBarker 7 magnet structure and a complementary Barker 7 magnet structure.Referring to FIG. 3A, note first that magnet structures 220 and 214 areno longer aligned (alternatively referred to as misaligned) in contrastwith FIG. 2H and complementary magnets 222 and 224 are no longeraligned, also in contrast to FIG. 2H. Instead, magnet 222 is inalignment with corresponding magnet 302 directly across the interfaceboundary. Referring generally to FIG. 3A-FIG. 3N, a Barker length 7 code(1, 1, 1, −1, −1, 1, −1) is used to determine the polarities and thepositions of magnets making up a first magnetic field emission structure220. Each magnet has the same or substantially the same magnetic fieldstrength (or amplitude), which for the sake of this example is provideda unit of 1 (where A=Attract, R=Repel, A=−R, A=1, R=−1). A secondmagnetic field emission structure that is identical to the first isshown in 13 different alignments in FIG. 3A through FIG. 3N relative tothe first magnetic field emission structure FIG. 3A. (Note that magnetstructure 220 is identical to magnet structure 214 in terms of magnetfield directions; however the interfacing poles are of oppositepolarity.) For each relative alignment, the number of magnets that repelplus the number of magnets that attract is calculated, where eachalignment has a total spatial force in accordance with a spatial forcefunction based upon the correlation function and magnetic fieldstrengths of the magnets. In other words, the total magnetic forcebetween the first and second magnet structures is determined as the sumfrom left to right along the structure of the individual forces, at eachmagnet position, of each magnet or magnet pair interacting with itsdirectly opposite corresponding magnet in the opposite magnet structure.Where only one magnet exists, the corresponding magnet is zero, and theforce is zero. Where two magnets exist, the force is R for equal polesor A for opposite poles. Thus, for FIG. 3A, the first six positions tothe left have no interaction. The one position in the center shows two“S” poles in contact for a repelling force of 1. The next six positionsto the right have no interaction, for a total force of 1R=−1, arepelling force of magnitude 1. The spatial correlation of the magnetsfor the various alignments is similar to radio frequency (RF) signalcorrelation in time, since the force is the sum of the products of themagnet strengths of the opposing magnet pairs over the lateral width ofthe structure. (Typically, correlation and autocorrelation may benormalized for a maximum peak of 1. This disclosure, however, uses anon-normalized formulation.) Thus,

$f = {\sum\limits_{{n = 1},N}\;{p_{n}q_{n}}}$

-   -   where,    -   f is the total magnetic force between the two structures,    -   n is the position along the structure up to maximum position N,        and    -   p_(n) are the strengths and polarities of the lower magnets at        each position n.    -   q_(n) are the strengths and polarities of the upper magnets at        each position n.

An alternative equation separate strength and polarity variables, asfollows:

$f = {\sum\limits_{{n = 1},N}\;{l_{n}p_{n}u_{n}q_{n}}}$

-   -   where,    -   f is the total magnetic force between the two structures,    -   n is the position along the structure up to maximum position N,    -   l_(n) are the strengths of the lower magnets at each position n,    -   p_(n) are the polarities (1 or −1) of the lower magnets at each        position n,    -   u_(n) are the strengths of the upper magnets at each position n,        and    -   q_(n) are the polarities (1 or −1) of the upper magnets at each        position n,        The above force calculations can be performed for each shift of        the two structures to plot a force vs. position function for the        two structures. The force vs. position function may        alternatively be called a spatial force function.

The total magnetic force is computed for each of the figures, FIG.3A-FIG. 3N and is shown with each figure. With the specific Barker codeused, it can be observed from the figures that the spatial force variesfrom −1 to 7, where the peak occurs when the two magnetic field emissionstructures are aligned such that their respective codes are aligned,FIG. 3G and FIG. 3H (FIG. 3G and FIG. 3H show the same alignment, whichis repeated for continuity between the two columns of figures). The offpeak spatial force, referred to as a side lobe force, varies from 0 to−1. As such, the spatial force function causes the magnetic fieldemission structures to generally repel each other unless they arealigned such that each of their magnets is correlated with acomplementary magnet (i.e., a magnet's South pole aligns with anothermagnet's North pole, or vice versa). In other words, the two magneticfield emission structures substantially correlate when they are alignedsuch that they substantially mirror each other.

FIG. 4A and FIG. 4B illustrate the normal force between variably codedmagnet structures for sliding offsets shown in FIGS. 3A-3N. FIG. 4Adepicts the sliding action shown in FIGS. 3A-3N in a single diagram. InFIG. 4A magnet structure 214 is stationary while magnet structure 220 ismoved across the top of magnet structure 214 in direction 408 accordingto scale 404. Magnet structure 220 is shown at position 1 according toindicating pointer 406, which moves with the left magnet of structure220. As magnet structure 220 is moved from left to right, the totalattraction and repelling forces are determined and plotted in the graphof FIG. 4B.

FIG. 4B shows a graph of the normal (perpendicular) magnetic forcesbetween the two magnet structures as a function of position of themagnet structure 220 relative to magnet structure 214. The plot of FIG.4B summarizes the results of FIGS. 3A-3N. The total normal force 402acting on all magnets alternates between a value of −1, and 0,indicating a repelling force equal to a single magnet pair acting acrossthe interface boundary or neutral force, to a force of +7 indicating theforce of all seven magnet pairs acting in attraction. Note that amovement of one magnet width from position 7 to position 6 changes theforce from 7 to 0. One more step to position 5 results in net repellingforce of −1. In contrast, note the performance of uniformly coded 7length magnet structures as shown in FIGS. 5A and 5B.

FIG. 5A and FIG. 5B show the normal force produced by a pair of 7 lengthuniformly coded magnet structures. FIG. 5A depicts the sliding action ofthe uniformly coded magnet pairs in the manner of FIG. 4A showing thebase structure, complementary structure, scale, pointer, and slidingdirection. FIG. 5B shows the net normal force 502 as a function ofposition of structure 504. Note that the force begins at 1 andincrements by one for each incremental position to a maximum of 7 andthen decreases again. The value does not reach zero or go negative forthe overlapping range shown.

Thus, one can appreciate by comparing the performance of FIG. 4B withFIG. 5B that the coded magnet structure pair 214 and 220 may have a muchmore precise lock-in performance at the alignment position than theuniformly coded structure pair 212 and 504. For example, a disturbancethat overcomes half the magnetic force would deviate FIG. 4B by only ahalf magnet position, whereas, the same disturbance would deflect thestructure of FIG. 5B by half of the width of the whole magnet structure.In addition, note the coded magnet structure of FIG. 4B indicatesmisalignments (positions 1-6 and 8-13) by zero attraction or evenrepelling forces; whereas the uniformly coded structure of FIG. 5Balways attracts. It should be noted that both the variably coded anduniformly coded magnet structures require a holding force since at leastone magnet of the structures oriented unnaturally.

The attraction functions of FIG. 4B, FIG. 5B and others in thisdisclosure are idealized, but illustrate the main principle and primaryperformance. The curves show the performance assuming equal magnet size,shape, and strength and equal distance between corresponding magnets.For simplicity, the plots only show discrete integer positions andinterpolate linearly. Actual force values may vary from the graph due tovarious factors such as diagonal coupling of adjacent magnets, magnetshape, spacing between magnets, properties of magnetic materials, etc.The curves also assume equal attract and repel forces for equaldistances. Such forces may vary considerably and may not be equaldepending on magnet material and field strengths. High coercive forcematerials typically perform well in this regard.

Comparing the variably coded structure of FIG. 4A with the uniformlycoded structure of FIG. 5A, one may note that the normal forcecharacteristic as a function of position FIG. 4B for the variably codedmagnet structure has a single maximum peak substantially equal instrength to the function (FIG. 5B) for the uniformly coded structure;however the width of the peak for the variably coded magnet structure isless than the width of the peak of the uniformly coded magnet structure,often less than half. The width of the peak may be measured at anyconvenient level, for example half of the peak strength. The width ofthe peak in FIG. 4B can be seen to be substantially equal to the widthof a peak for a single magnet. Substantially in the context of thisparagraph means in view of the considerations of the previous paragraph.

As mentioned earlier, this invention may be used with any magnet,whether permanent, electromagnet, or even with electric fields, however,for embodiments employing permanent magnets, the magnetic materials ofinterest may include, but are not limited to: Neodymium-Iron-Boron andrelated materials, Samarium Cobalt, Alnico, and Ceramic ferrites.Neodymium Iron Boron may refer to the entire range of rare earth ironboron materials. One important subset is based on the chemical formulaR₂Fe₁₄B, where R is Nd, Ce, or Pr. The magnet material may includemixtures of the different rare earth elements. Numerous methods ofmanufacture are known, each yielding different magnetic properties.Samarium Cobalt, Alnico and ceramic ferrites have been known longer andcan also yield magnets suitable for use with the present invention. Newmaterials and variations of the present materials are expected to bedeveloped that may also be used with the present invention.

Codes for use in constructing coded magnet structures may include anumber of codes known to mathematics and often applied to subjects suchas communication theory, radar and other technologies. A few codes areillustrated and exemplified herein, but many others may be equallyapplicable. Several codes exemplified herein include Barker codes,Kasami Codes, LFSR sequences, Walsh codes, Golomb ruler codes, andCostas arrays. Information on these codes is, at this time abundantlyavailable on the World Wide Web and in the technical literature.Articles from the site Wikipedia® have been printed and incorporatedherein by reference. Thus the articles “Barker Codes” Wikipedia, 2 Aug.2008, “Linear Feedback Shift Register”, Wikipedia, 11 Nov. 2008, “KasamiCode”, Wikipedka, 11 Jun. 2008, “Walsh code”, Wikipedia, 17 Sep. 2008,“Golomb Ruler”, 4 Nov. 2008, and “Costas Array”, Wikipedia 7 Oct. 2008are incorporated herein by reference in their entirety.

The examples so far in FIG. 3A-FIG. 3N, FIG. 4A, and FIG. 4B have usedthe Barker 7 code to illustrate the principles of the invention. Barkercodes have been found to exist in lengths up to 13. Table 1 shows Barkercodes up to length 13. Additional Barker codes may be generated bycyclic shifts (register rotations) or negative polarity (multiply by −1)transformations of the codes of Table 1. The technical literatureincludes Barker-like codes of even greater length. Barker codes offer apeak force equal to the length and a maximum misaligned force of 1 or−1. Thus, the ratio of peak to maximum misaligned force is length/1 or−length/1.

TABLE 1 Barker Codes Length Codes 2 +1 −1 +1 +1 3 +1 +1 −1 4 +1 −1 +1 +1+1 −1 −1 −1 5 +1 +1 +1 −1 +1 7 +1 +1 +1 −1 −1 +1 −1 11 +1 +1 +1 −1 −1 −1+1 −1 −1 +1 −1 13 +1 +1 +1 +1 +1 −1 −1 +1 +1 −1 +1 −1 +1

Numerous other codes are known in the literature for low autocorrelationwhen misaligned and may be used for magnet structure definition asillustrated with the Barker 7 code. Such codes include, but are notlimited to maximal length PN sequences, Kasami codes, Golomb ruler codesand others. Codes with low non-aligned autocorrelation offer theprecision lock at the alignment point as shown in FIG. 4B.

Pseudo Noise (PN) and noise sequences also offer codes with lownon-aligned autocorrelation. Most generally a noise sequence orpseudo-noise sequence is a sequence of 1 and −1 values that is generatedby a true random process, such as a noise diode or other natural source,or is numerically generated in a deterministic (non random) process thathas statistical properties much like natural random processes. Thus,many true random and pseudo random process may generate suitable codesfor use with the present invention. Random processes, however willlikely have random variations in the sidelobe amplitude i.e., nonaligned force as a function of distance from alignment; whereas, Barkercodes and others may have a constant amplitude when used as cyclic codes(FIG. 6B). One such family is maximal length PN codes generated bylinear feedback shift registers (LFSR). LFSR codes offer a family ofvery long codes with a constant low level non-aligned cyclicautocorrelation. The codes come in lengths of powers of two minus oneand several different codes of the same length are generally availablefor the longer lengths. LFSR codes offer codes in much longer lengthsthan are available with Barker codes. Table 2 summarizes the propertiesfor a few of the shorter lengths. Extensive data on LFSR codes isavailable in the literature.

TABLE 2 LFSR Sequences Number of Length of Number of Example Stagessequences Sequences feedback 2 3 1 1, 2 3 7 2 2, 3 4 15 2 3, 4 5 31 6 3,5 6 63 6 5, 6 7 127 18 6, 7 8 255 16 4, 5, 6, 8 9 511 48 5, 9 10 1023 60 7, 10

The literature for LFSR sequences and related sequences such as Gold andKasami often uses a 0, 1 notation and related mathematics. The twostates 0, 1 may be mapped to the two states −1, +1 for use with magnetpolarities. An exemplary LFSR sequence for a length 4 shift registerstarting at 1,1,1,1 results in the feedback sequence: 000100110101111,which may be mapped to: −1, −1, −1, +1, −1, −1, +1, +1, −1, +1, −1, +1,+1, +1, +1. Alternatively, the opposite polarities may be used or acyclic shift may be used.

Code families also exist that offer a set of codes that may act as aunique identifier or key, requiring a matching part to operate thedevice. Kasami codes and other codes can achieve keyed operation byoffering a set of codes with low cross correlation in addition to lowautocorrelation. Low cross correlation for any non-aligned offset meansthat one code of the set will not match and thus not lock with astructure built according to the another code in the set. For example,two structures A and A*, based on code A and the complementary code A*,will slide and lock at the precision lock point. Two structures B and B*from the set of low cross correlation codes will also slide and locktogether at the precision alignment point. However, code A will slidewith low attraction at any point but will not lock with code B* becauseof the low cross correlation properties of the code. Thus, the code canact like a key that will only achieve lock when matched with a like(complementary) pattern.

Kasami sequences are binary sequences of length 2^(N) where N is an eveninteger. Kasami sequences have low cross-correlation values approachingthe Welch lower bound for all time shifts and may be used as cycliccodes. There are two classes of Kasami sequences—the small set and thelarge set.

The process of generating a Kasami sequence starts by generating amaximum length sequence a_(n), where n=1.2^(N)−1. Maximum lengthsequences are cyclic sequences so a_(n) is repeated periodically for nlarger than 2^(N)−1. Next, we generate another sequence b_(n) bygenerating a decimated sequence of a_(n) at a period of q=2^(N/2)+1,i.e., by taking every q^(th) bit of a_(n). We generate b_(n) byrepeating the decimated sequence q times to form a sequence of length2^(N)−1. We then cyclically shift b_(n) and add to a_(n) for theremaining 2^(N)−2 non repeatable shifts. The Kasami set of codescomprises a_(n), a_(n)+b_(n), and the cyclically shifted a_(n)+(shiftb_(n)) sequences. This set has 2^(N/2) different sequences. A firstcoded structure may be based on any one of the different sequences and acomplementary structure may be the equal polarity or negative polarityof the first coded structure, depending on whether repelling orattracting force is desired. Neither the first coded structure nor thecomplementary structure will find strong attraction with any of theother codes in the 2^(N/2) different sequences. An exemplary 15 lengthKasami small set of four sequences is given in Table 3 below. The 0,1notation may be transformed to −1,+1 as described above. Cyclic shiftsand opposite polarity codes may be used as well.

TABLE 3 Exemplary Kasami small set sequences. Sequence K1 0 0 0 1 0 0 11 0 1 0 1 1 1 1 K2 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 K3 1 1 0 0 1 0 0 0 0 01 1 0 0 1 K4 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0

Other codes, such as Walsh codes and Hadamard codes, offer sets of codeswith perfectly zero cross correlation across the set of codes whenaligned, but possibly high correlation performance when misaligned. Suchcodes can provide the unique key function when combined with mechanicalconstraints that insure alignment. Exemplary Walsh codes are as follows:

Denote W(k, n) as Walsh code k in n-length Walsh matrix. It means thek-th row of Hadamard matrix H(m), where n=2m, m an integer. Here k couldbe 0, 1, . . . , n−1. A few Walsh codes are shown in Table 4.

TABLE 4 Walsh Codes Walsh Code Code W(0, 1) 1 W(0, 2) 1, 1 W(1, 2) 1, −1W(0, 4) 1, 1, 1, 1 W(1, 4) 1, −1, 1, −1 W(2, 4) 1, 1, −1, −1 W(3, 4) 1,−1, −1, 1 W(0, 8) 1, 1, 1, 1, 1, 1, 1, 1 W(1, 8) 1, −1, 1, −1, 1, −1, 1,−1 W(2, 8) 1, 1, −1, −1, 1, 1, −1, −1 W(3, 8) 1, −1, −1, 1, 1, −1, −1, 1W(4, 8) 1, 1, 1, 1, −1, −1, −1, −1 W(5, 8) 1, −1, 1, −1, −1, 1, −1, 1W(6, 8) 1, 1, −1, −1, −1, −1, 1, 1 W(7, 8) 1, −1, −1, 1, −1, 1, 1, −1

In use, Walsh codes of the same length would be used as a set of codesthat have zero interaction with one another, i.e., Walsh code W(0,8)will not attract or repel any of the other codes of length 8 whenaligned. Alignment should be assured by mechanical constraints becauseoff alignment attraction can be great.

Codes may be employed as cyclic codes or non-cyclic codes. Cyclic codesare codes that may repetitively follow another code, typicallyimmediately following with the next step after the end of the last code.Such codes may also be referred to as wrapping or wraparound codes.Non-cyclic codes are typically used singly or possibly used repetitivelybut in isolation from adjacent codes. The Barker 7 code example of FIG.4A and FIG. 4B is a non-cyclic use of the code; whereas the example ofFIG. 6A and FIG. 6B is a cyclic use of the same code.

FIG. 6A and FIG. 6B show a cyclic implementation of a Barker 7 code.Referring to FIG. 6A, the base magnet structure comprise three repeatedBarker 7 coded magnet structures 214 a, 214 b, and 214 c, whereadditional Barker 7 coded magnet structures not shown precede and followthe three repeated Barker 7 coded magnet structure 214 a, 214 b, and 214c. Each Barker code portion 214 a, 214 b, or 214 c, as well as 220 maybe termed a code modulo. The span across a single modulo 214 a is amodulo span for the magnet structure. Pointer 606 indicates the positionof structure 220 with reference to scale 604. The complementary magnetstructure 220 slides along the base magnet structure, and the net forceis recorded for each position. As shown, complementary magnet structure220 is located at relative alignment position 7, which corresponds tothe first peak force spike in FIG. 6B.

FIG. 6B shows the normal magnetic force 602 as a function of positionfor FIG. 6A. Note that the total force shows a peak of 7 each time thesliding magnet structure 220 aligns with the underlying Barker 7 patternin a similar manner as previously described for FIG. 4B. Note however inFIG. 6B, the misaligned positions (positions 1-6 for example) show aconstant −1 indicating a repelling force of one magnet pair. Incontrast, FIG. 4B alternates between zero and −1 in the misalignedregion, where the alternating values are the result of their beingrelative positions of non-cyclic structures where magnets do not have acorresponding magnet with which to pair up In magnet structures, cycliccodes may be placed in repeating patterns to form longer patterns or maycycle back to the beginning of the code as in a circle or racetrackpattern. As such, cyclic codes are useful on cylindrically orspherically shaped objects.

It may be observed in the embodiment of FIG. 6A that the base magnetstructure 214 a-214 c may be of differing length than the complementarystructure 220. Also that the base magnetic structure 214 a-214 c maycomprise repeating segments 214 a wherein each repeating segmentcomprises a non-repeating sequence of magnet polarities. It may befurther appreciated that the complementary structure may also compriserepeating segments of sequences of non repeating magnet polarities.

FIG. 7A and FIG. 7B show two magnet structures 704 a, 704 b coded usinga Golomb ruler code. A Golomb ruler is a set of marks on a ruler suchthat no two marks are the same distance from any other two marks. Twoidentical Golomb rulers may be slid by one another with only one mark ata time aligning with the other ruler except at the sliding point whereall marks align. Referring to FIG. 7A, magnets 702 of structure 704 aare placed at positions 0, 1, 4, 9 and 11, where all magnets areoriented in the same polarity direction. Pointer 710 indicates theposition of cluster 704 a against scale 708. The stationary basestructure 704 b uses the same relative magnet positioning patternshifted to begin at position 11.

FIG. 7B shows the normal (perpendicular) magnetic force 706 as afunction of the sliding position between the two structures 704 a and704 b of FIG. 7A. Note that only one magnet pair lines up between thetwo structures for any sliding position except at position 5 and 17,where no magnet pairs line up, and at position 11, where all five magnetpairs line up. Because all magnets are in the same direction, themisaligned force value is 1, indicating attraction. Alternatively, someof the magnet polarities may be reversed according to a second code orpattern (with a complementary pattern on the complementary magnetstructure) causing the misaligned force to alternate between 1 and −1,but not to exceed a magnitude of 1. The aligned force would remain at 5if both magnet structures have the same polarity pattern. It may also beappreciated that a magnet substructure spaced according to a Golombruler code may be paired with a passive (unmagnetized) ferromagneticsubstructure of the same Golomb ruler pattern and the combined structurewould have essentially the same force function as if both substructureswere magnets. For example, if the top magnet structure of FIG. 7A were asequence of magnets and the bottom structure were a sequence of softiron bars, a maximum attraction value of 5 would occur at alignment, theoffset attraction would be a maximum of 1, and the system forces wouldbe described by the graph as shown in FIG. 7B. Table 5 shows a number ofexemplary Golomb ruler codes. Golomb rulers of higher orders up to 24can be found in the literature.

TABLE 5 Golomb Ruler Codes order length marks 1 0 0 2 1 0 1 3 3 0 1 3 46 0 1 4 6 5 11 0 1 4 9 11 0 2 7 8 11 6 17 0 1 4 10 12 17 0 1 4 10 15 170 1 8 11 13 17 0 1 8 12 14 17 7 25 0 1 4 10 18 23 25 0 1 7 11 20 23 25 01 11 16 19 23 25 0 2 3 10 16 21 25 0 2 7 13 21 22 25

Golomb ruler codes offer a force ratio according to the order of thecode, e.g., for the order 5 code of FIG. 7A, the aligned force to thehighest misaligned force is 5:1. Where the magnets are of differingpolarities, the ratio may be positive or negative, depending on theshift value.

Two Dimensional Magnet Structures

The one dimensional magnet structures described so far serve toillustrate the basic concepts, however, it is often desirable todistribute magnets over a two dimensional area rather than in a singleline. Several approaches are available. In one approach, known twodimensional codes may be used. In another approach, two dimensionalcodes may be generated from one dimensional codes. In still anotherapproach, two dimensional codes may be found by numerical methods.

FIG. 8A-FIG. 8E show various exemplary two dimensional code structuresin accordance with the present invention. The magnet structures of FIG.2A through FIG. 7A are shown and described with respect to relativemovement in a single dimension, i.e., along the interface boundary inthe direction of the code. Some applications utilize such magnetstructures by mechanically constraining the relative motion to thesingle degree of freedom being along the interface boundary in thedirection of the code. Other applications allow movement perpendicularto the direction of the code along the interface boundary, or both alongand perpendicular to the direction of the code, offering two degrees offreedom. Still other applications may allow rotation and may bemechanically constrained to only rotate around a specified axis, thushaving a single degree of freedom (with respect to movement along theinterface boundary.) Other applications may allow two lateral degrees offreedom with rotation adding a third degree of freedom. Mostapplications also operate in the spacing dimension to attract or repel,hold or release. The spacing dimension is usually not a dimension ofinterest with respect to the code; however, some applications may payparticular attention to the spacing dimension as another degree offreedom, potentially adding tilt rotations for six degrees of freedom.For applications allowing two lateral degrees of freedom special codesmay be used that place multiple magnets in two dimensions along theinterface boundary.

Costas arrays are one example of a known two dimensional code. CostasArrays may be considered the two dimensional analog of the onedimensional Golomb rulers. Lists of known Costas arrays are available inthe literature. In addition, Welch-Costas arrays may be generated usingthe Welch technique. Alternatively, Costas arrays may be generated usingthe Lempel-Golomb technique.

FIG. 8A shows an exemplary Costas array. Referring to FIG. 8A, the grid802 shows coordinate positions. The “+” 804 indicates a locationcontaining a magnet, blank 806 in a grid location indicates no magnet.Each column contains a single magnet, thus the array of FIG. 8A may bespecified as {2,1,3,4}, specifying the row number in each successivecolumn that contains a magnet. Additional known arrays up to order 5(five magnets in a 5×5 grid) are as follows, where N is the order:

N=1

{1}

N=2

{1,2} {2,1}

N=3

{1,3,2} {2,1,3} {2,3,1} {3,1,2}

N=4

{1,2,4,3} {1,3,4,2} {1,4,2,3} {2,1,3,4} {2,3,1,4} {2,4,3,1} {3,1,2,4}{3,2,4,1} {3,4,2,1} {4,1,3,2} {4,2,1,3} {4,3,1,2}

N=5

{1,3,4,2,5} {1,4,2,3,5} {1,4,3,5,2} {1,4,5,3,2} {1,5,3,2,4} {1,5,4,2,3}{2,1,4,5,3} {2,1,5,3,4} {2,3,1,5,4} {2,3,5,1,4} {2,3,5,4,1} {2,4,1,5,3}{2,4,3,1,5} {2,5,1,3,4} {2,5,3,4,1} {2,5,4,1,3} {3,1,2,5,4} {3,1,4,5,2}{3,1,5,2,4} {3,2,4,5,1} {3,4,2,1,5} {3,5,1,4,2} {3,5,2,1,4} {3,5,4,1,2}{4,1,2,5,3} {4,1,3,2,5} {4,1,5,3,2} {4,2,3,5,1} {4,2,5,1,3} {4,3,1,2,5}{4,3,1,5,2} {4,3,5,1,2} {4,5,1,3,2} {4,5,2,1,3} {5,1,2,4,3} {5,1,3,4,2}{5,2,1,3,4} {5,2,3,1,4} {5,2,4,3,1} {5,3,2,4,1}

Additional Costas arrays may be formed by flipping the array (reversingthe order) vertically for a first additional array and by flippinghorizontally for a second additional array and by transposing(exchanging row and column numbers) for a third additional array. Costasarray magnet structures may be further modified by reversing or notreversing the polarity of each successive magnet according to a secondcode or pattern as previously described with respect to Golomb rulercodes.

FIG. 8B illustrates the generation of a two dimensional magnet structureby replicating a one dimensional code pattern. Referring to FIG. 8B,each row is a linear magnet sequence arranged according to the Barker 7code. N rows are stacked in parallel to form a 7×N array 808. The 7×Narray 808 shown will have Barker 7 code properties (FIG. 4B) whensliding left to right and simple magnet properties (FIG. 5B) whensliding up and down (when paired with a complementary structure). Bothleft and right movement and up and down movement as shown on the page ina plan view as shown in FIG. 8B or as depicted in other figures may alsobe referred to as lateral movement.

FIG. 8C illustrates a 7×7 magnet structure with successively rotatedBarker 7 codes in each successive row. Referring to FIG. 8C, the 7×7magnet structure 808 a is formed by varying the code pattern from row torow. The top row is the Barker 7 pattern 214. The next row is the Barkerpattern shifted left with the value that is shifted out of the left mostposition shifted into the right most position. This operation is oftentermed rotation with respect to digital shift register operations. Thusthe magnet pattern for each successive row is a rotate 1 position leftversion of the row immediately above. It may be appreciated that thehorizontal performance of the structure of FIG. 8C remains similar tothe Barker 7 pattern; whereas; the vertical pattern is no longer thesimple uniformly coded pattern of FIG. 8B. In fact, the vertical patternnow comprises various rotations of the Barker 7 pattern.

FIG. 8D illustrates an exemplary slide-lock pattern based on FIG. 8C.Referring to FIG. 8D, a 19×7 two-way (right and left) slide lock code810 is produced by starting with a copy of the 7×7 code 808 a and thenby adding the leftmost 6 columns (808 c) of the 7×7 code 808 a to theright of the code 808 a and the rightmost 6 columns (808 d) of the 7×7code 808 a to the left of the code 808 a. As such, as the mirror image808 b of structure 808 a slides from side-to-side, all 49 magnets of 808b are in contact with the base structure 810 producing the force curveof FIG. 6B from positions 1 to 13, with the magnitude scale multipliedby seven due to the seven parallel rows of magnets. Thus, when structure808 b is aligned with the portion 808 a of structure 810 correspondingto 808 b's mirror image, the two structures will lock with an attractiveforce of 49, while when the structure 808 b is slid left or right to anyother position, the two structures 808 b, 810 will produce a repel forceof −7. If structure 808 b were to be replaced with a second structurehaving the same coding as portion 808 a of the structure 810, then whenaligned the two structures will repel with a force of −49, while whenthe second structure 808 a is slid left or right to any other position,the two structures 808 b, 810 will produce an attractive force of 7.

FIG. 8E illustrates an exemplary hover code. Referring to FIG. 8E thehover code 806 is produced by placing two code modulos of 808 aside-by-side and then removing the first and last columns of theresulting structure, i.e., the right most six columns of 808 a (808 c)are placed to the left of the left most six columns of a second copy of808 a, (808 d). As such, a mirror image 808 b can be moved across theresulting magnetic field emission structure 812 from one end to theother end and at all times achieve a spatial force function of −7,indicating a repelling force, potentially allowing the structure 808 bto hover over the base 812.

FIG. 9A-FIG. 9F illustrate additional two dimensional codes derived fromthe single dimension Barker 7 code. Referring to FIG. 9A, The code 808 aof FIG. 8C is shown with each row identified by a reference number insequence 901-907. Also note that each column is a rotation of a Barker 7code running downward as indicated by the respective down arrows alongthe bottom of the figure. FIG. 9B illustrates a first variation 910generated by reordering the rows of FIG. 9A. Observe that the columnsare also rotations of Barker 7 codes running in the downward direction,just as in FIG. 9A, but shifted. FIG. 9C illustrates a second variation911 generated by reordering the rows of FIG. 9A. In FIG. 9C, not allcolumns form Barker 7 codes (indicated by X). One column is a Barker 7code running downward, indicated by the down arrow. Three columns are aBarker 7 codes running upward, indicated by the up arrows. FIG. 9Dillustrates a third variation 912 generated by reordering the rows ofFIG. 9A. In FIG. 9D, all columns form Barker 7 codes running upward, asindicated by the up arrows.

FIG. 9E illustrates a fourth alternative 913 where three of the rows of808 a are multiplied by −1, i.e., reversed in polarity. Row 902A, 904Aand 906 a are reversed in polarity from rows 902, 904, and 906respectively. Note that the code of 808 a has 28 “+” magnets and 21 “−”magnets; whereas, alternative 913 has 25 “+” magnets and 24 “−”magnets—a nearly equal number. Thus, the far field magnetic field fromstructure 913 will nearly cancel to zero, which can be valuable in someapplications. FIG. 9F illustrates a fifth alternative 914 where three ofthe rows are reversed in direction. Rows 902 b, 904 b and 906 b arereversed from 902, 904, and 906 respectively.

FIG. 9G illustrates a further alternative using four codes of low mutualcross correlation. Generally, two dimensional codes may be generated bycombining multiple single dimensional codes. In particular, the singledimensional codes may be selected from sets of codes with known lowmutual cross correlation. Gold codes and Kasami codes are two examplesof such codes, however, other code sets may also be used. Referring toFIG. 9G four rows 908-911 of 15 length Kasami codes are used in theexample. Because the rows have low cross correlation and lowautocorrelation, shifts either laterally or up and down (as viewed onthe page) or both will result in low magnetic force.

Additional magnet structures having low magnetic force with a firstmagnet structure generated from a set of low cross correlation codes maybe generated by reversing the polarity of the magnets or by usingdifferent subsets of the set of available codes. For example, rows 908and 909 may form a first magnet structure and rows 910 and 911 may forma second magnet structure. The complementary magnet structure of thefirst magnet structure will have low force reaction to the second magnetstructure, and conversely, the complementary magnet structure of thesecond magnet structure will have a low force reaction to the firstmagnet structure. Alternatively, if lateral or up and down movement isrestricted, an additional low interaction magnet structure may begenerated by shifting (rotating) the codes or changing the order of therows. Movement may be restricted by such mechanical features asalignment pins, channels, stops, container walls or other mechanicallimits.

More generally FIG. 9A-FIG. 9G illustrate that two dimensional codes maybe generated from one dimensional codes by assembling successive rows ofone dimensional codes and that multiple different two dimensional codesmay be generated by varying each successive row by operations includingbut not limited to changing the order, shifting the position, reversingthe direction, and/or reversing the polarity.

FIG. 10A and FIG. 10B depict a magnetic field emission structure 1002comprising nine magnets in three parallel columns of three magnets each,with the center column shifted by one half position. Referring to FIG.10A the magnetic field emission structure 1002 is a magnet structure ofnine magnets showing the end of each magnet with the polarity marked oneach magnet. The positions of the magnets are shown against a coordinategrid 1004. The center column of magnets forms a linear sequence of threemagnets each centered on integer grid positions. Two additional columnsof magnets are placed on each side of the center column and on adjacentinteger column positions, but the row coordinates are offset by one halfof a grid position. More particularly, the structure comprises ninemagnets at relative coordinates of +1(0,0), −1(0,1), +1(0,2), −1(1,0.5),+1(1,1.5), −1(1,2.5), +1(2,0), −1(2,1), +1(2,2), where within thenotation s(x,y), “s” indicates the magnet strength and polarity and“(x,y)” indicates x and y coordinates of the center of the magnetrelative to a reference position (0,0). The magnet structure, accordingto the above definition is then placed such that magnet +1(0,0) isplaced at location (9,9.5) in the coordinate frame 1004 of FIG. 10A.

When paired with a complementary structure, and the force is observedfor various rotations of the two structures around the center coordinateat (10, 11), the structure 1002 has a peak spatial force when(substantially) aligned and has relatively minor side lobe strength atany rotation off alignment.

FIG. 10B depicts the spatial force function 1006 of the magnetic fieldemission structure 1002 with respect to lateral translations of thecomplementary magnetic field emission structure. The graph 1006 of FIG.10B shows the force for lateral translations of the two structures withno rotation. The peak force 1008 occurs when substantially aligned.

FIG. 11A-FIG. 11C depict an exemplary code 1102 intended to produce amagnetic field emission structure having a first stronger lock whenaligned with its mirror image magnetic field emission structure and asecond weaker lock when rotated 90° relative to its mirror imagemagnetic field emission structure. FIG. 11A shows magnet structure 1102is against a coordinate grid 1104. The magnet structure 1102 of FIG. 11Acomprises magnets at positions: −1(3,7), −1(4,5), −1(4,7), +1(5,3),+1(5,7), −1(5,11), +1(6,5), −1(6,9), +1(7,3), −1(7,7), +1(7,11),−1(8,5), −1(8,9), +1(9,3), −1(9,7), +1(9,11), +1(10,5),−1(10,9)+1(11,7). Additional field emission structures may be derived byreversing the direction of the x coordinate or by reversing thedirection of the y coordinate or by transposing the x and y coordinates.

FIG. 11B depicts spatial force function 1106 of a magnetic fieldemission structure 1102 interacting with its mirror image(complementary) magnetic field emission structure. The peak occurs whensubstantially aligned.

FIG. 11C depicts the spatial force function 1108 of magnetic fieldemission structure 1102 interacting with its mirror magnetic fieldemission structure after being rotated 90°. FIG. 11C shows the forcefunction for lateral translations without further rotation. The peakoccurs when substantially aligned but one structure rotated 90°.

FIGS. 12A-12I depict the exemplary magnetic field emission structure1102 a and its mirror image magnetic field emission structure 1102 b andthe resulting spatial forces produced in accordance with their variousalignments as they are twisted relative to each other, i.e., rotatedaround an axis perpendicular to the interface plane and through thecenter of the structures 1102 a and 1102 b. In FIG. 12A, the magneticfield emission structure 1102 a and the mirror image magnetic fieldemission structure 1102 b are aligned producing a peak spatial force. InFIG. 12B, the mirror image magnetic field emission structure 1102 b isrotated clockwise slightly relative to the magnetic field emissionstructure 1102 a and the attractive force reduces significantly. In FIG.12C, the mirror image magnetic field emission structure 1102 b isfurther rotated and the attractive force continues to decrease. In FIG.12D, the mirror image magnetic field emission structure 1102 b is stillfurther rotated until the attractive force becomes very small, such thatthe two magnetic field emission structures are easily separated as shownin FIG. 12E. Given the two magnetic field emission structures heldsomewhat apart as in FIG. 12F, the structures can be moved closer androtated towards alignment producing a small spatial force as in FIG.12F. The spatial force increases as the two structures become more andmore aligned in FIGS. 12G and 12H and a peak spatial force is achievedwhen aligned as in FIG. 121. It should be noted that the direction ofrotation was arbitrarily chosen and may be varied depending on the codeemployed. Additionally, the mirror image magnetic field emissionstructure 1102 b is the mirror of magnetic field emission structure 1102a resulting in an attractive peak spatial force. The mirror imagemagnetic field emission structure 1102 b could alternatively be codedsuch that when aligned with the magnetic field emission structure 1102 athe peak spatial force would be a repelling force in which case thedirections of the arrows used to indicate amplitude of the spatial forcecorresponding to the different alignments would be reversed such thatthe arrows faced away from each other.

Computer Search for Codes

Additional codes including polarity codes, ruler or spacing codes orcombinations of ruler and polarity codes of one or two dimensions may befound by computer search. The computer search may be performed byrandomly or pseudorandomly or otherwise generating candidate patterns,testing the properties of the patterns, and then selecting patterns thatmeet desired performance criteria. Exemplary performance criteriainclude, but are not limited to, peak force, maximum misaligned force,width of peak force function as measured at various offset displacementsfrom the peak and as determined as a force ratio from the peak force,polarity of misaligned force, compactness of structure, performance ofcodes with sets of codes, or other criteria. The criteria may be applieddifferently for different degrees of freedom.

Additional codes may be found by allowing magnets to have differentstrengths, such as multiple strengths (e.g., 2, 3, 7, 12) or fractionalstrengths (e.g. ½, 1.7, 3.3).

In accordance with one embodiment, a desirable coded magnet structuregenerally has a non-regular pattern of magnet polarities and/orspacings. The non-regular pattern may include at least one adjacent pairof magnets with reversed polarities, e.g., +, −, or −, +, and at leastone adjacent pair of magnets with the same polarities, e.g., +,+ or −,−. Quite often code performance can be improved by having one or moreadditional adjacent magnet pairs with differing polarities or one ormore additional adjacent magnet pairs with the same polarities.Alternatively, or in combination, the coded magnet structure may includemagnets having at least two different spacings between adjacent magnetsand may include additional different spacings between adjacent magnets.In some embodiments, the magnet structure may comprise regular ornon-regular repeating subsets of non-regular patterns.

Exemplary Uses For Magnet Structures

FIG. 13A-FIG. 13D depict various exemplary mechanisms that can be usedwith field emission structures and exemplary tools utilizing fieldemission structures in accordance with the present invention. FIG. 13Adepicts two magnetic field emission structures 1102 a and 1102 b. One ofthe magnetic field emission structures 1102 b includes a turningmechanism 1300 that includes a tool insertion slot 1302. Both magneticfield emission structures include alignment marks 1304 along an axis1303. A latch mechanism such as the hinged latch clip 1305 a and latchknob 1305 b may also be included preventing movement (particularlyturning) of the magnetic field emission structures once aligned. Underone arrangement, a pivot mechanism (not shown) could be used to connectthe two structures 1102 a, 1102 b at a pivot point such as at pivotlocation marks 1304 thereby allowing the two structures to be moved intoor out of alignment via a circular motion about the pivot point (e.g.,about the axis 1303).

FIG. 13B depicts a first circular magnetic field emission structurehousing 1306 and a second circular magnetic field emission structurehousing 1308 configured such that the first housing 1306 can be insertedinto the second housing 1308. The second housing 1308 is attached to analternative turning mechanism 1310 that is connected to a swivelmechanism 1312 that would normally be attached to some other object.Also shown is a lever 1313 that can be used to provide turning leverage.

FIG. 13C depicts an exemplary tool assembly 1314 including a drill headassembly 1316. The drill head assembly 1316 comprises a first housing1306 and a drill bit 1318. The tool assembly 1314 also includes a drillhead turning assembly 1320 comprising a second housing 1308. The firsthousing 1306 includes raised guides 1322 that are configured to slideinto guide slots 1324 of the second housing 1308. The second housing1308 includes a first rotating shaft 1326 used to turn the drill headassembly 1316. The second housing 1308 also includes a second rotatingshaft 1328 used to align the first housing 1306 and the second housing1308.

FIG. 13D depicts an exemplary clasp mechanism 1390 including a firstpart 1392 and a second part 1394. The first part 1392 includes a firsthousing 1308 supporting a first magnetic field emission structure. Thesecond part 1394 includes a second housing 1306 used to support a secondmagnetic field emission structure. The second housing 1306 includesraised guides 1322 that are configured to slide into guide slots 1324 ofthe first housing 1308. The first housing 1308 is also associated with amagnetic field emission structure slip ring mechanism 1396 that can beturned to rotate the magnetic field emission structure of the first part1392 so as to align or misalign the two magnetic field emissionstructures of the clasp mechanism 1390. Generally, all sorts of claspmechanisms can be constructed in accordance with the present inventionwhereby a slip ring mechanism can be turned to cause the clasp mechanismto release. Such clasp mechanisms can be used as receptacle plugs,plumbing connectors, connectors involving piping for air, water, steam,or any compressible or incompressible fluid. The technology is alsoapplicable to Bayonette Neil-Concelman (BNC) electronic connectors,Universal Serial Bus (USB) connectors, and most any other type ofconnector used for any purpose.

The gripping force described above can also be described as a matingforce. As such, in certain electronics applications this ability toprovide a precision mating force between two electronic parts or as partof a connection may correspond to a desired characteristic, for example,a desired impedance. Furthermore, the invention is applicable toinductive power coupling where a first magnetic field emission structurethat is driven with AC will achieve inductive power coupling whenaligned with a second magnetic field emission structure made of a seriesof solenoids whose coils are connected together with polaritiesaccording to the same code used to produce the first magnetic fieldemission structure. When not aligned, the fields will close onthemselves since they are so close to each other in the driven magneticfield emission structure and thereby conserve power. Ordinaryinductively coupled systems' pole pieces are rather large and cannotconserve their fields in this way since the air gap is so large.

FIG. 14A-FIG. 14E illustrate exemplary ring magnet structures based onlinear codes. Referring to FIG. 14A, ring magnet structure 1402comprises seven magnets arranged in a circular ring with the magnet axesperpendicular to the plane of the ring and the interface surface isparallel to the plane of the ring. The exemplary magnet polarity patternor code shown in FIG. 14A is the Barker 7 code. One may observe the “+,+, +, −, −, +, −” pattern beginning with magnet 1404 and movingclockwise as indicated by arrow 1406. A further interesting feature ofthis configuration is that the pattern may be considered to then wrap onitself and effectively repeat indefinitely as one continues around thecircle multiple times. Thus, one could use cyclic linear codes arrangedin a circle to achieve cyclic code performance for rotational motionaround the ring axis. The Barker 7 base pattern shown would be pairedwith a complementary ring magnet structure placed on top of the magnetstructure face shown. As the complementary ring magnet structure isrotated, the force pattern can be seen to be equivalent to that of FIGS.6A and 6B because the complementary magnet structure is alwaysoverlapping a head to tail Barker 7 cyclic code pattern.

FIG. 14A also illustrates exemplary optional mechanical restraints thatmay be used with ring magnet structures. In one embodiment, a centralspindle 1424, alternatively referred to as a shaft or pin may beinstalled with the first magnet structure and a mating bearing or socketmay be provided with the complementary magnet structure to constrain themotion to rotation only without lateral motion. The pin may be short sothat the restraint is operative only when the magnet structures are inproximity and the pin is coupled to the socket. Alternatively, a shell1426 or housing may be provided with the first magnet structure thatmates with a circular plug surrounding the ring with the complementarymagnet structure. See FIG. 13D for additional shell structures. The pin1424 and/or shell 1426 may also be used to provide greater lateral loadbearing capability for the assembly.

FIG. 14B shows a magnet structure based on the ring code 1402 of FIG.14A with an additional magnet in the center. Magnet structure 1408 hasan even number of magnets. At least two features of interest aremodified by the addition of the magnet 1410 in the center. For rotationabout the ring axis, one may note that the center magnet pair (in thebase and in the complementary structure) remain aligned for allrotations. Thus, the center magnet pair add a constant attraction orrepelling force. Thus, the graph of FIG. 6B could be shifted from arepelling force of −1 and attracting force of 7 to a repelling force ofzero and an attracting force of 8. In other words, yielding a neutralforce when not aligned. Note also that the central magnet pair may beany value, for example −3, yielding an equal magnitude repelling andattracting force of −4 and +4, respectively.

In a further alternative, a center magnet 1410 may be paired in thecomplementary structure with a non-magnetized ferromagnetic material,such as a magnetic iron or steel piece. The center magnet would thenprovide attraction, no matter which polarity is chosen for the centermagnet.

A second feature of the center magnet of FIG. 14B is that for a value of−1 as shown, the total number of magnets in the positive direction isequal to the total number of magnets in the negative direction. Thus, inthe far field, the magnetic field approaches zero, minimizingdisturbances to such things as magnetic compasses and the like. Moregenerally the total strength of magnets in one direction may becancelled by the total strength of magnets in the opposite direction,regardless of the number of magnets. (For example, the center magnet mayhave any desired strength.)

FIG. 14C illustrates two concentric rings, each based on a linear cycliccode, resulting in magnet structure 1412. An inner ring 1402 is as shownin FIG. 14A, beginning with magnet 1404. An outer ring is also a Barker7 code beginning with magnet 1414. Beginning the outer ring on theopposite side as the inner ring keeps the plusses and minuses somewhatlaterally balanced.

FIG. 14D illustrates the two concentric rings of FIG. 14C wherein theouter ring magnets are the opposite polarity of adjacent inner ringmagnets resulting in magnet structure 1416. The inner ring Barker 7begins with magnet 1404. The outer ring Barker 7 is a negative Barker 7beginning with magnet 1418. Each outer ring magnet is the opposite ofthe immediate clockwise inner ring adjacent magnet. Since the far fieldmagnetic field is cancelled in adjacent pairs, the field decays asrapidly as possible from the equal and opposite magnet configuration.More generally, linear codes may be constructed of opposite polaritypairs to minimize far field magnetic effects.

FIG. 14E illustrates a Barker 7 inner ring and Barker 13 outer ring. TheBarker 7 begins with magnet 1404 and the Barker 13 begins with magnet1422. The result is composite ring magnet structure 1420.

Although Barker codes are shown in FIGS. 14A-14E, other codes may beuses as alternative codes or in combination with Barker codes,particularly in adjacent rings. Maximal Length PN codes or Kasami codes,for example, may form rings using a large number of magnets. One or tworings are shown, but any number of rings may be used. Although the ringstructure and ring codes shown are particularly useful for rotationalsystems that are mechanically constrained to prevent lateral movement asmay be provided by a central shaft or external sleeve, the rings mayalso be used where lateral position movement is permitted. It may beappreciated that a single ring, in particular, has only one or twopoints of intersection with another single ring when not aligned. Thus,non-aligned forces would be limited by this geometry in addition to codeperformance.

In one embodiment, the structures of FIG. 14A-14E may be used for areleasable magnetic attachment. The number and strength of componentmagnets may be selected as needed or desired to establish the magneticattachment strength for a given application. The attachment strength isthe total magnetic attraction when in the attachment configuration,i.e., when the component magnets of the magnet structure andcomplementary magnet structure are aligned and most or all magnet pairsare attracting. The number of magnets and code as well as additionalmagnets (such as magnet 1410 in FIG. 14B) may be selected to set therelease strength and release characteristic function (for example, theside lobe portion of FIG. 4B). The release strength is typically anormal force that allows convenient removal of the magnetic structure.The release configuration is a position, typically in the side lobeportion of a characteristic function (e.g., FIG. 4B) that allows forrelease. The release strength may be a reduced attraction force, arepelling force, or zero. The release strength is typically less thanthe attachment strength, preferably less than half the attachmentstrength, and often substantially equal to a single component magnet ofthe magnet structure. Typically, a release configuration ischaracterized by having sufficient numbers magnets in the magnetstructure opposing the polarity of the magnets in the complementarymagnet structure so that the total attraction force is reduced to allowseparation of the two magnet structures.

FIG. 15A-FIG. 15E depict the components and assembly of an exemplarycovered structural assembly. FIG. 15A depicts a first elongatedstructural member 1502 having magnetic field emission structures 1504 oneach of two ends and also having an alignment marking 1506 (“AA”), whichcould also be “aa”. FIG. 15B also depicts a second elongated structuralmember 1508 having magnetic field emission structures 1510 on both endsof one side. The magnetic field emission structures 1504 and 1510 areconfigured such that they can be aligned to attach the first and secondstructural members 1502 and 1508. FIG. 15C further depicts a structuralassembly 1512 including two of the first elongated structural members1502 attached to two of the second elongated structural members 1508whereby four magnetic field emission structure pairs 1504/1510 arealigned. FIG. 15D includes a cover panel 1514 having four magnetic fieldemission structures 1102 a that are configured to align with fourmagnetic field emission structures 1102 b to attach the cover panel 1514to the structural assembly 1512 to produce a covered structural assembly1516 shown in FIG. 15E.

Generally, the ability to easily turn correlated magnetic structuressuch that they disengage is a function of the torque easily created by aperson's hand by the moment arm of the structure. The larger it is, thelarger the moment arm, which acts as a lever. When two separatestructures are physically connected via a structural member, as with thecover panel 1514, the ability to use torque is defeated because themoment arms are reversed. This reversal is magnified with eachadditional separate structure connected via structural members in anarray. The force is proportional to the distance between respectivestructures, where torque is proportional to force times radius. As such,in one embodiment, the magnetic field emission structures of the coveredstructural assembly 1516 include a turning mechanism enabling one of thepaired field emission structures to be rotated to be aligned ormisaligned in order to assemble or disassemble the covered structuralassembly. In another embodiment, the magnetic field emission structuresdo not include a turning mechanism and thus require full force fordecoupling.

FIG. 16A and FIG. 16B illustrate relative force and distancecharacteristics of large magnets as compared with small magnets. FIG.16A depicts an oblique projection of a first pair of magnetic fieldemission structures 1602 a and 1602 b. FIG. 16B depicts a second pair ofmagnetic field emission structures 1604 a and 1604 b each havinginternal magnets indicated by dashed lines.

As shown, the first pair of magnetic field emission structures 1602 aand 1602 b have a relatively small number of relatively large (andstronger) magnets when compared to the second pair of magnetic fieldemission structures 1604 a and 1604 b that have a relatively largenumber of relatively small (and weaker) magnets. For this figure, thepeak spatial force for each of the two pairs of magnetic field emissionstructures 1602 a/1602 b and 1604 a/1604 b are the same. However, thedistances D1 and D2 at which the magnetic fields of each of the pairs ofmagnetic field emission structures substantially interact depends on thestrength of the magnets and the area over which they are distributed. Assuch, the much larger surface of the second magnetic field emissionstructure 1604 a/1602 b having much smaller magnets will notsubstantially attract until much closer than that of first magneticfield emission structure 1602 a/1602 b. In addition, it can beappreciated that, for a substantially random coded magnet structure,adjacent magnets will likely be of opposite polarity. Thus, when thedistance D1 or D2 becomes significant relative to the magnet width orlateral spacing, the magnet begins to interact with magnets of theopposite polarity, further reducing the attracting force of thestructure. This magnetic strength per unit area attribute as well as amagnetic spatial frequency (i.e., the number of magnetic reversals perunit area) can be used to design structures to meet safety requirements.For example, two magnetic field emission structures 1604 a/1604 b can bedesigned to not have unsafe attraction at a spacing equal to the widthof a finger to prevent damage from clamping a finger between themagnets.

FIG. 16C depicts an exemplary magnetic field emission structure 1606made up of a sparse array of large magnetic sources 1608 combined with alarge number of smaller magnetic sources 1610 whereby alignment with amirror image magnetic field emission structure would be provided by thelarge sources and a repel force would be provided by the smallersources. Generally, as was the case with FIG. 16A, the larger (i.e.,stronger) magnets achieve a significant attraction force (or repellingforce) at a greater separation distance than smaller magnets. Because ofthis characteristic, combinational structures having magnetic sources ofdifferent strengths can be constructed that effectively have two (ormore) spatial force functions corresponding to the different levels ofmagnetic strengths employed. As the magnetic field emission structuresare brought closer together, the spatial force function of the strongestmagnets is first to engage and the spatial force functions of the weakermagnets will engage when the magnetic field emission structures aremoved close enough together at which the spatial force functions of thedifferent sized magnets will combine. Referring back to FIG. 16B, thesparse array of stronger magnets 1608 is coded such that it cancorrelate with a mirror image sparse array of comparable magnets.However, the number and polarity of the smaller (i.e., weaker) magnets1610 can be tailored such that when the two magnetic field emissionstructures are substantially close together, the magnetic force of thesmaller magnets can overtake that of the larger magnets 1608 such thatan equilibrium will be achieved at some distance between the twomagnetic field emission structures. As such, alignment can be providedby the stronger magnets 1608 but contact of the two magnetic fieldemission structures can be prevented by the weaker magnets 1610.Similarly, the smaller, weaker magnets can be used to add extraattraction strength between the two magnetic field emission structures.

One skilled in the art may recognize based on the teachings herein thatmany different combinations of magnets having different strengths can beoriented in various ways to achieve desired spatial forces as a functionof orientation and separation distance between two magnetic fieldemission structures. For example, a similar aligned attract-repelequilibrium might be achieved by grouping the sparse array of largermagnets 1608 tightly together in the center of magnetic field emissionstructure 1606. Moreover, combinations of correlated and non-correlatedmagnets can be used together, for example, the weaker magnets 1610 ofFIG. 16B may all be uncorrelated magnets. Furthermore, one skilled inthe art will recognize that such equilibrium enables frictionlesstraction (or hold) forces to be maintained and that such techniquescould be employed for many of the exemplary drawings provided herein.

FIG. 17A-FIG. 17C illustrate several exemplary cylinder and spherearrangements, some arrangements including coupling with linear trackstructures. FIG. 17A depicts two concentric cylinders for concentricrotational alignment. The two cylinders each have a field emissionstructure and the complementary field emission structure disposed aroundthe cylinder surface and directed across an interface gap between thetwo cylinders. The cylinders will see a relative torque related to theslope of the force graph (for example FIG. 6B). Thus, one cylinder maybe used to couple to and drive the other. Any number of code repeatsegments may be provided. In particular, the code may be chosen to haveonly one non-repeated segment (sequence of magnets) and thus only onelock point. In a second embodiment, one of the cylinders may havepermanent magnets forming the field emission structure and the secondcylinder may utilize electromagnets. The electromagnets may be driven toposition or move the code pattern around the cylinder and thus drive thefirst cylinder synchronous with the electromagnet code position. Again,the electromagnets may have any number of code segments around thecylinder down to including one segment, which is typically difficult toachieve with common synchronous or stepping type motors.

In a further alternative, cylinder 1706 may couple to a flat track 1708.Neglecting cylinder 1704 for the moment, cylinder 1706 may have a fieldemission structure on the outside and 1708 may have a complementarystructure. Cylinder 1706 may then grip track 1708 and roll along track1708 as a guide, or may drive or be driven by track 1708. Again thetrack or cylinder may utilize electromagnets to move the pattern toeffect a moving drive. Since the hold-down force equals the tractionforce, these gears can be loosely connected and still give positive,non-slipping rotational accuracy. Correlated surfaces can be perfectlysmooth and still provide positive, non-slip traction. As such, they canbe made of any substance including hard plastic, glass, stainless steelor tungsten carbide. In contrast to legacy friction-based wheels thetraction force provided by correlated surfaces is independent of thefriction forces between the traction wheel and the traction surface andcan be employed with low friction surfaces. Devices moving about basedon magnetic traction can be operated independently of gravity forexample in weightless conditions including space, underwater, verticalsurfaces and even upside down.

FIG. 17B depicts an arrangement where a first magnetic field emissionstructure 1722 wraps around two cylinders 1702 a and 1702 b such that amuch larger portion 1724 of the first magnetic field emission structure1722 is in contact with a second magnetic field emission structure 1728by comparison with the contact of 1702 with 1708 of FIG. 17A. As such,the larger portion 1724 directly corresponds to a larger gripping force.

If the surface in contact with the cylinder is in the form of a belt,then the traction force can be made very strong and still benon-slipping and independent of belt tension. It can replace, forexample, toothed, flexible belts that are used when absolutely noslippage is permitted. In a more complex application the moving belt canalso be the correlating surface for self-mobile devices that employcorrelating wheels. If the conveyer belt is mounted on a movable vehiclein the manner of tank treads then it can provide formidable traction toa correlating surface or to any of the other rotating surfaces describedhere.

FIG. 17C illustrates two spheres, an outer sphere 1712 containing aninner sphere 1714. The outer sphere has a field emission structure 1716and the inner sphere has a complementary field emission structure. Thus,the two spheres may be coupled and synchronized. One may utilizeelectromagnets to drive the other.

FIGS. 18A through 18H provide a few more examples of how magnetic fieldsources can be arranged to achieve desirable spatial force functioncharacteristics. FIG. 18A depicts an exemplary magnetic field emissionstructure 1800 made up of rings about a circle. As shown, each ringcomprises one magnet having an identified polarity. Similar structurescould be produced using multiple magnets in each ring, where each of themagnets in a given ring is the same polarity as the other magnets in thering, or each ring could comprise correlated magnets. Generally,circular rings, whether single layer or multiple layer, and whether withor without spaces between the rings, can be used for electrical, fluid,and gas connectors, and other purposes where they could be configured tohave a basic property such that the larger the ring, the harder it wouldbe to twist the connector apart. As shown in FIG. 18B, one skilled inthe art would recognize that a hinge 1802 could be constructed usingalternating magnetic field emission structures attached two objectswhere the magnetic field emission structures would be interleaved sothat they would align (i.e., effectively lock) but they would stillpivot about an axis extending though their innermost circles. FIG. 18Cdepicts an exemplary magnetic field emission structure 1804 havingsources resembling spokes of a wheel. FIG. 18D depicts an exemplarymagnetic field emission structure 1806 resembling a rotary encoder whereinstead of on and off encoding, the sources are encoded such that theirpolarities vary. The use of a magnetic field emission structure inaccordance with the present invention instead of on and off encodingshould eliminate alignment problems of conventional rotary encoders.

FIG. 18E depicts an exemplary magnetic field emission structure havingsources arranged as curved spokes 1808. FIG. 18F depicts an exemplarymagnetic field emission structure made up of hexagon-shaped sources1810. FIG. 18G depicts an exemplary magnetic field emission structuremade up of triangular sources 1812. FIG. 18H depicts an exemplarymagnetic field emission structure made up of arrayed diamond-shapedsources 1814. Generally, the sources making up a magnetic field emissionstructure can have any shape and multiple shapes can be used within agiven magnetic field emission structure. Under one arrangement, one ormore magnetic field emission structures correspond to a Fractal code.

FIG. 19A through FIG. 19G depict exemplary embodiments of twodimensional coded magnet structures. Referring to FIG. 19A, theexemplary magnet structure 1900 comprises two Barker coded magnetsubstructures 214 and 1902. Substructure 214 comprises magnets withpolarities determined by a Barker 7 length code arranged horizontally(as viewed on the page). Substructure 1902 comprises magnets withpolarities also determined by a Barker 7 length code, but arrangedvertically (as viewed on the page) and separated from substructure 214.In use, structure 1900 is combined with a complementary structure ofidentical shape and complementary magnet polarity. It can be appreciatedthat the complementary structure would have an attracting (or repelling,depending on design) force of 14 magnet pairs when aligned. Uponshifting the complementary structure to the right one magnet widthsubstructure 214 and the complementary portion would look like FIG. 3Fand have a force of zero. Substructure 902 would be shifted off to theside with no magnets overlapping producing a force of zero. Thus, thetotal from both substructures 214 and 902 would be zero. As thecomplementary structure is continued to be shifted to the right,substructure 214 would generate alternately zero and −1. The resultinggraph would look like FIG. 4B except that the peak would be 14 insteadof 7. It can be further appreciated that similar results would beobtained for vertical shifts due to the symmetry of the structure 1900.Diagonal movements where the complementary structure for 1902 overlaps214 can only intersect one magnet at a time. Thus, the peak twodimensional nonaligned force is 1 or −1. Adding rotational freedom canpossibly line up 1902 with 214 for a force of 7, so the code of FIG. 19Aperforms best where rotation is limited.

FIG. 19B depicts a two dimensional coded magnet structure comprising twocodes with a common end point component. Referring to FIG. 19B, thestructure 1903 comprises structure 214 based on a Barker 7 code runninghorizontally and structure 1904 comprising six magnets that togetherwith magnet 1906 form a Barker 7 code running vertically. Magnet 1906being common to both Barker sequences. Performance can be appreciated tobe similar to FIG. 19A except the peak is 13.

FIG. 19C depicts a two dimensional coded magnet structure comprising twoone dimensional magnet structures with a common interior pointcomponent. The structure of FIG. 19C comprises structure 214 based on aBarker 7 code running horizontally and structure 1908 comprising sixmagnets that together with magnet 1910 form a Barker 7 code runningvertically. Magnet 1910 being common to both Barker sequences.Performance can be appreciated to be similar to FIG. 19A except the peakis 13. In the case of FIG. 19C diagonal shifts can overlap two magnetpairs.

FIG. 19D depicts an exemplary two dimensional coded magnet structurebased on a one dimensional code. Referring to FIG. 214, a square isformed with structure 214 on one side, structure 1904 on another side.The remaining sides 1912 and 1914 are completed using negative Barker 7codes with common corner components. When paired with an attractioncomplementary structure, the maximum attraction is 24 when aligned and 2when not aligned for lateral translations in any direction includingdiagonal. Further, the maximum repelling force is −7 when shiftedlaterally by the width of the square. Because the maximum magnitudenon-aligned force is opposite to the maximum attraction, manyapplications can easily tolerate the relatively high value (comparedwith most non-aligned values of 0, ±1, or ±2) without confusion. Forexample, an object being placed in position using the magnet structurewould not stick to the −7 location. The object would only stick to the+1, +2 or +24 positions, very weakly to the +1 or +2 positions and verystrongly to the +24 position, which could easily be distinguished by theinstaller.

FIG. 19E illustrates a two dimensional code derived by using multiplemagnet substructures based on a single dimension code placed atpositions spaced according to a Golomb Ruler code. Referring to FIG.19E, five magnet substructures 1920-1928 with polarities determinedaccording to a Barker 7 code are spaced according to an order 5 Golombruler code at positions 0, 1, 4, 9, and 11 on scale 1930. The totalforce in full alignment is 35 magnet pairs. The maximum non-alignedforce is seven when one of the Barker substructures lines up withanother Barker 7 substructure due to a horizontal shift of thecomplementary code. A vertical shift can result in −5 magnet pairs.Diagonal shifts are a maximum of −1.

The exemplary structures of FIG. 19A-FIG. 19E are shown using Barker 7codes, the structures may instead use any one dimension code, forexample, but not limited to random, pseudo random, LFSR, Kasami, Gold,or others and may mix codes for different legs. The codes may be run ineither direction and may be used in the negative version (multiplied by−1.) Further, several structures are shown with legs at an angle of 90degrees. Other angles may be used if desired, for example, but notlimited to 60 degrees, 45 degrees, 30 degrees or other angles. Otherconfigurations may be easily formed by one of ordinary skill in the artby replication, extension, substitution and other teachings herein.

FIG. 19F and FIG. 19G illustrate two dimensional magnet structures basedon the two dimensional structures of FIG. 19A through FIG. 19E combinedwith Costas arrays. Referring to FIG. 19F, the structure of FIG. 19F isderived from the structure 1911 of FIG. 19C replicated 1911 a-1911 d andplaced at code locations 1914 based on a coordinate grid 1916 inaccordance with exemplary Costas array of FIG. 8A. The structure of FIG.19G is derived using FIG. 19C and FIG. 8A as described for FIG. 19Fexcept that the scale (relative size) is changed. The structure 1911 ofFIG. 19C is enlarged to generate 1911 e-1911 h, which have been enlargedsufficiently to overlap at component 1918. Thus, the relative scale canbe adjusted to trade the benefits of density (resulting in more forceper area) with the potential for increased misaligned force.

Summary of Coded Magnet Patterns

Magnet patterns have been shown for basic linear and two dimensionalarrays. Linear codes may be applied to generate linear magnet arraysarranged in straight lines, curves, circles, or zigzags. The magneticaxes may be axial or radial to the curved lines or surfaces. Twodimensional codes may be applied to generate two dimensional magnetarrays conforming to flat or curved surfaces, such as planes, spheres,cylinders, cones, and other shapes. In addition, compound shapes may beformed, such as stepped flats and more.

Magnet applications typically involve mechanical constraints such asrails, bearings, sleeves, pins, etc that force the assembly to operatealong the dimensions of the code. Several known types of codes can beapplied to linear, rotational, and two-dimensional configurations. Someconfigurations with lateral and rotational and vertical and tilt degreesof freedom may be satisfied with known codes tested and selected for theadditional degrees of freedom. Computer search can also be used to findspecial codes.

Thus, the application of codes to generate arrangements of magnets withnew interaction force profiles and new magnetic properties enables newdevices with new capabilities, examples of which will now be disclosed.

Stepping Motors With Coded Pole Patterns

FIG. 20A and FIG. 20B illustrate a model of the torque generated by thestepping motor of FIG. 1A at full step aligned positions. FIG. 20A showsthe rotor poles in row A and the stator poles in row B. A scale 2002 isshown for movement of the rotor magnets through one rotation, sevenpositions. Stator magnets are indicated by a scale 0-15. The number ofstator poles is actually seven (see ref 2004). The additional positionsshow the repeating cyclic rotational pattern. Positions 8-14 (see 2006)represent the same poles as positions 1-7. With the rotor in position 1as shown the torque may be approximated by observing that opposingmagnet pairs in the rotor and stator, being aligned and centered,generate no torque, only attraction or repelling forces. Diagonallyopposing adjacent poles may generate torque. Diagonally adjacent polesare assigned an attracting or repelling value of +1 or −1 respectivelydepending on whether they are in the same or opposing directions.Because of the distance, the remaining poles may be ignored. Thus, thetorque on the rotor may be determined by summing the forces of theadjacent poles of the stator on each pole of the rotor.

$T = {\sum\limits_{N}{S_{LF}\left( {{A_{n}B_{n}} - {A_{n}B_{n + 1}}} \right)}}$

Where,

T is the rotor torque,

N is the number of poles (magnets) in the rotor,

S_(LF) is the magnet strength for full step movement,

A_(n) is the rotor magnet polarity for position n, and

B_(n) is the stator magnet polarity for position n.

FIG. 20B is a table showing the seven torque pair sums 2010 for each ofthe seven aligned rotor positions 2002 in one rotation (rotor magnetsaligned directly opposite stator magnets). Column 2002 is the rotorposition. Column 2008 is the torque on each rotor magnet. Column 2010 isthe sum for that position. Referring to table FIG. 20B, position 1 showsa torque balance with two positions each generating opposite torque andthree positions generating no torque. Position 1 is the aligned positionwith the pole pattern for the rotor matching the stator. Position 2 isone pole position advanced to the right. In position 2, four polepositions have a + polarity of two magnet pairs each for a total of 8magnet pairs. Three positions have a torque of zero. Thus, there is astrong torque of 8 magnet pairs to return the rotor to the alignedposition 1. Positions 3-6 show balanced torque and position 7, which isthe same as one position to the left (position 0) shows a negativetorque. Also returning the rotor to the aligned position 1. Thus therotor has one stable locked position, position 1 where the adjacentpositions 2 and 7 return the rotor to position 1. the other positionshave neutral torque and provide no stability. The rotor may move withoutresisting torque among the remaining positions 3-6. When the rotor movesfrom position 3 toward position 2, the rotor is quickly “captured” andmoved to position 1.

FIG. 21A and FIG. 21B illustrate a model of the torque generated by thestepping motor of FIG. 1A at half step positions. FIG. 21A shows therotor positioned at a half step to the right of the position shown inFIG. 20A. The rotor makes full step increments beginning with a halfstep offset. A similar calculation of torque to FIG. 20B is provided.This time the adjacent magnets provide torque. No magnets are aligned.The torque at half step may be different from the torque at full step sothe strength constant S_(LH) is provided to account for the difference.

$T = {\sum\limits_{N}{S_{LH}\left( {{A_{n}B_{n}} - {A_{n}B_{n + 1}}} \right)}}$

Where,

T is the rotor torque,

N is the number of poles (magnets) in the rotor,

S_(LH) is the magnet strength for half step movement,

A_(n) is the rotor magnet polarity for position n plus a half step, and

B_(n) is the stator magnet polarity for position n.

FIG. 21B shows the torque summations 2010 for the seven magnet polepairs 2008 for each of the seven rotor positions 2002. Positions 1 and 7show a torque of 8 in a direction to return the rotor to the alignedposition, which is a half step before position 1 (or a half step afterposition 7) on the half step diagram. The remaining positions 2-6 showbalanced torque. Thus, aligned position 1 of FIG. 20A is the only stablelocked in position where a disturbance is met with a torque to return tothe position.

FIG. 22 is a table illustrating the torque patterns for stepping motorsas in FIG. 1 constructed using various alternative codes. FIG. 22 showsthe torques computed relative to the stable aligned position 2202indicated by the arrows at the bottom. Note that for each of the codesthe stable position is flanked by high torque positions that return therotor to the stable position. Alternatively, the polarities of thestator may be reversed to generate an unstable equilibrium positionflanked by positions that repel from the unstable position. The tableincludes a Barker, length 7, Barker length 13, PN length 15, and Golombcode.

The Golomb ruler code may be specified as a five magnet, twelveposition, or eleven length code.

Composite Patterns

In one embodiment, the stator may be driven by a composite patterncomprising the sum of one or more shifted code patterns.

FIG. 23 illustrates an exemplary single or composite pattern drivearchitecture. Referring to FIG. 23, a code pattern is loaded intoregister 2301 and a rotated copy is transferred to register 2302 and afurther rotated copy is transferred to register 2303. The threeregisters are bitwise fed to the summation networks 2308 which feeddrivers 2310 which drive each pole 2312 of the stator, i.e., bit 1 ofeach register is fed to summation network 1 to be summed and the sumdrives pole 1 of the stator and so on for the remaining poles. Anynumber of registers may be used and each may have a different gain or beshifted by any desired amount. Several examples follow.

FIG. 24 illustrates an exemplary torque vs. position pattern for asingle pattern. Thus, FIG. 7 is for a 15 length Barker or PN code usinga single register.

FIG. 25 illustrates an exemplary torque vs. position pattern for acomposite pattern comprising the sum of two single patterns. The twopatterns are two PN codes offset by a shift of one pole position.

FIG. 26-FIG. 33 illustrate exemplary torque vs. position pattern forcomposite patterns comprising various sums of single patterns. FIGS.26-34 show the 15 length PN pattern shifted and summed according to afour digit key 2401 for each graph. The key 2401 is shown to the left ofeach graph. The key is four integers representing four shift positionsand the associated gain. For example, the key for FIG. 31 is 1221indicating a gain of 1 for the first position, 2 for a shift of 1, 2 fora shift of 2, and 1 for a shift of 3. The summation result is applied tothe rotor to find the torque as a function of rotation angle at theinteger positions shown. It can be appreciated that numerous compositefunctions can be generated by summing multiple code patterns.

FIG. 34A and FIG. 34B illustrate an exemplary vernier design andillustrates an exemplary compound pole pattern and illustrates anexemplary compound pole pattern applied to a vernier design. FIG. 34Aillustrates a vernier pole design with the rotor having a differentspacing from the stator. FIG. 34B illustrates a compound pole designwith three magnets per major pole and one magnet per minor pole. Themajor poles may be driven according to a first code and the magnets maybe driven by a second code. Thus each magnet is driven by the product ofthe code for the major pole and the minor pole. Each code may have apolarity and an amplitude for each code position. In one embodiment, aPN code or Barker code uses magnets of a single strength and the codespecifies the polarity only.

FIG. 35 illustrates various actual torque vs. rotation curves availablewith different pole piece designs. The simplified analysis used forFIGS. 20A, 20B, 21A and 21B gives a first order estimate of the torqueprofile (torque vs rotation angle). In practice, the pole design mayinfluence the profile as well. Pole width and spacing may vary thetorque profile from a lower and broader pattern to a sharper andstronger pattern. FIG. 35 depicts two exemplary estimated curvesrelative to a half pole and full pole rotation of the rotor.

Using The Stepping Motor In New Applications

In use, the stepping motor may be used to generate a torque profile thatallows free rotation of the rotor for any angle until the rotor is nearthe alignment position. When the rotor is near alignment, the rotorfalls as if into a notch and locks into synchronization with the stator.

In a further application, the stepping motor has only one synchronizedposition and thus, to the extent the rotor can be assumed to besynchronized, the rotor position will be absolutely known. Conventionalstepping motors have multiple ambiguous positions around thecircumference of the rotor. In one alternative embodiment, however thecoded stepping motor may employ more than one code modulo around therotor and thus have more than one lock in point around the rotor.

In one method of capturing the rotor, the stator drive may sweep a fullcircle to ensure capture of the rotor. From that point on, the rotor maybe assumed to be captured and synchronized with the stator.

In a further variation, an arbitrary torque profile may be generated bysumming a number of code patterns to generate a composite pattern. Inparticular, the torque profile patterns as shown in FIGS. 24-33 may begenerated. Similar profiles may be generated using codes of differentlengths.

The motor may be used for a number of specialized applications requiringunique drive characteristics. These specialized drive requirements mayarise in manufacturing machines, coin operated vending machines,automotive devices, appliances and other devices and machines.

In one example, a clock may be driven by a stepping motor with codedpoles. The clock represents a further variation in the invention. It maybe necessary to implement a number of code positions that are differentfrom the positions available from a code set. For example PN codes comein 2^(n)−1 lengths. Thus for the clock, a 63 length code may be theclosest available. In one embodiment, the designer may choose to utilize60 bits of the 63 bit length code for the 60 positions representing the60 seconds or 60 minutes of the clock. The application can likelytolerate the slight error introduced by truncating the code. Similarly,in another application 70 positions may be implemented by padding thecode with zeroes or utilizing 7 bits of the code to fill in the space.

In a further exemplary alternative, for the clock, a 63 pole motor maybe implemented, but the drive may be modified by using a variant of FIG.24 drive using a weighted sum of two copies of the code shifted by oneposition from one another to interpolate between the 63 pole positionsto yield 60 steps, i.e., each step would advance by 63/60 th or 1.05pole positions. Thus the drive would be:n=trunc(1.05S)w=1.05S−nd _(k)=(1−w)PN63(k+n)+wPN63(n+1)where,S is the step from zero to 59, affording 60 steps,n is the integer number of shifts of the code needed,trunc( ) is an integer truncation rounding function returning theinteger part,w is the fraction part of the truncation to be used as a weightingfactor,d_(k) is the drive for pole k, k=0 to 62, for 63 poles, andPN63( ) is the selected 63 length code function; the sums (k+n) and(n+1) are modulo 63.

In a further variation, nonlinear interpolation effects due to poleshape and other factors may be compensated by adjusting the weightfactor, w.

Thus, the drive moves the rotor 1.05 pole positions per step.

In a similar manner, dials, meters, gauges, valves and other actuatorsmay be driven using the above principles.

CONCLUSION

The present invention has been described above with the aid offunctional building blocks illustrating the performance of specifiedfunctions and relationships thereof. The boundaries of these functionalbuilding blocks have been arbitrarily defined herein for the convenienceof the description. Alternate boundaries can be defined so long as thespecified functions and relationships thereof are appropriatelyperformed. Any such alternate boundaries are thus within the scope andspirit of the claimed invention. One skilled in the art will recognizethat these functional building blocks can be implemented by discretecomponents, application specific integrated circuits, processorsexecuting appropriate software and the like or any combination thereof.

While various embodiments of the present invention have been describedabove, it should be understood that they have been presented by way ofexample only, and not limitation. Thus, the breadth and scope of thepresent invention should not be limited by any of the above-describedexemplary embodiments, but should be defined only in accordance with thefollowing claims and their equivalents.

1. A stepping motor comprising: a rotor having a predetermined number ofrotor poles, said rotor having a rotational axis; a first stator havinga number of stator poles corresponding to said predetermined number ofrotor poles; said stator poles disposed to magnetically interact withsaid rotor poles to generate a torque on said rotor tending to rotatesaid rotor around said rotational axis in accordance with an electricaldrive applied to said stator poles; wherein said rotor poles areconfigured in accordance with a magnetic pattern based on a code;wherein said code has an autocorrelation function having a singlemaximum peak magnitude value per code modulo and a plurality of offmaximum peak magnitude values; wherein a greatest peak magnitude valueof said plurality of off maximum peak magnitude values is less than onehalf of the single maximum peak magnitude value.
 2. A stepping motorcomprising: a rotor having a predetermined number of rotor poles, saidrotor having a rotational axis; a first stator having a number of statorpoles corresponding to said predetermined number of rotor poles; saidstator poles disposed to magnetically interact with said rotor poles togenerate a torque on said rotor tending to rotate said rotor around saidrotational axis in accordance with an electrical drive applied to saidstator poles; wherein said rotor poles are configured in accordance witha magnetic pattern based on a code; wherein said code has anautocorrelation function having a single maximum peak per code moduloand a plurality of off maximum peak values wherein said off maximum peakvalues are less than one half of the maximum peak; wherein the code is aBarker code.
 3. A stepping motor comprising: a rotor having apredetermined number of rotor poles, said rotor having a rotationalaxis; a first stator having a number of stator poles corresponding tosaid predetermined number of rotor poles; said stator poles disposed tomagnetically interact with said rotor poles to generate a torque on saidrotor tending to rotate said rotor around said rotational axis inaccordance with an electrical drive applied to said stator poles;wherein said rotor poles are configured in accordance with a magneticpattern based on a code; wherein said code has an autocorrelationfunction having a single maximum peak per code modulo and a plurality ofoff maximum peak values wherein said off maximum peak values are lessthan one half of the maximum peak; wherein the code is a PN sequencecode.
 4. A stepping motor comprising: a rotor having a predeterminednumber of rotor poles, said rotor having a rotational axis; a firststator having a number of stator poles corresponding to saidpredetermined number of rotor poles; said stator poles disposed tomagnetically interact with said rotor poles to generate a torque on saidrotor tending to rotate said rotor around said rotational axis inaccordance with an electrical drive applied to said stator poles;wherein said rotor poles are configured in accordance with a magneticpattern based on a code; wherein said code has an autocorrelationfunction having a single maximum peak per code modulo and a plurality ofoff maximum peak values wherein said off maximum peak values are lessthan one half of the maximum peak; wherein the code is a Golomb rulercode.
 5. The stepping motor in accordance with claim 1, wherein the codehas a length greater than four.
 6. The stepping motor in accordance withclaim 1, further including a drive system; wherein said drive system isconfigured to drive said first stator in accordance with said code. 7.The stepping motor in accordance with claim 1, further including a drivesystem; wherein said drive system is configured to drive said rotor inaccordance with at least two copies of said code said at least twocopies of said code shifted relative to one another.
 8. The steppingmotor in accordance with claim 1, wherein said magnetic pattern isrepeated around said rotor one or more times.
 9. The stepping motor inaccordance with claim 1, wherein said rotor comprises a disk or acylinder.
 10. The stepping motor in accordance with claim 1, furtherincluding at least one additional stator coupled to said rotor, said atleast one additional stator shifted in phase by a partial pole positionrelative to a phase of said first stator.
 11. A method for operating astepping motor, said stepping motor having a predetermined number ofpoles in a first stator and corresponding number of poles in a rotormagnetically coupled to said first stator, said method comprising thesteps of: producing a magnetic field pattern in said rotor in accordancewith a code; producing a magnetic field pattern in said first stator inaccordance with said code; and sequentially shifting said magnetic fieldpattern in at least one of said rotor or said first stator to effectrotation of said rotor; wherein said rotor poles are configured inaccordance with a magnetic pattern based on a code; wherein said codehas an autocorrelation function having a single maximum peak magnitudevalue per code modulo and a plurality of off maximum peak magnitudevalues; wherein a greatest peak magnitude value of said plurality of offmaximum peak magnitude values is less than one half of the singlemaximum peak magnitude value.
 12. A method for operating a steppingmotor, said stepping motor having a predetermined number of poles in afirst stator and corresponding number of poles in a rotor magneticallycoupled to said first stator, said method comprising the steps of:producing a magnetic field pattern in said rotor in accordance with acode; producing a magnetic field pattern in said first stator inaccordance with said code; and sequentially shifting said magnetic fieldpattern in at least one of said rotor or said first stator to effectrotation of said rotor; wherein said code has an autocorrelationfunction having a single maximum peak per code modulo and a plurality ofoff maximum peak values wherein the off maximum peak values are lessthan one half of the maximum peak; wherein the code is a Barker code.13. A method for operating a stepping motor, said stepping motor havinga predetermined number of poles in a first stator and correspondingnumber of poles in a rotor magnetically coupled to said first stator,said method comprising the steps of: producing a magnetic field patternin said rotor in accordance with a code; producing a magnetic fieldpattern in said first stator in accordance with said code; andsequentially shifting said magnetic field pattern in at least one ofsaid rotor or said first stator to effect rotation of said rotor;wherein said code has an autocorrelation function having a singlemaximum peak per code modulo and a plurality of off maximum peak valueswherein the off maximum peak values are less than one half of themaximum peak; wherein the code is a PN sequence code.
 14. A method foroperating a stepping motor, said stepping motor having a predeterminednumber of poles in a first stator and corresponding number of poles in arotor magnetically coupled to said first stator, said method comprisingthe steps of: producing a magnetic field pattern in said rotor inaccordance with a code; producing a magnetic field pattern in said firststator in accordance with said code; and sequentially shifting saidmagnetic field pattern in at least one of said rotor or said firststator to effect rotation of said rotor; wherein said code has anautocorrelation function having a single maximum peak per code moduloand a plurality of off maximum peak values wherein the off maximum peakvalues are less than one half of the maximum peak; wherein the code is aGolomb ruler code.
 15. The method in accordance with claim 11, whereinthe code has a length greater than four.
 16. The method in accordancewith claim 11, further including driving said first stator in accordancewith said code.
 17. The method in accordance with claim 11, furtherincluding: driving said first stator in accordance with at least twocopies of said code shifted relative to one another.
 18. The method inaccordance with claim 11, further including repeating said magneticpattern one or more times around said rotor.
 19. The method inaccordance with claim 11, wherein said rotor comprises a disk or acylinder.
 20. The method in accordance with claim 11, further includingcoupling at least one additional stator to said rotor, said at least oneadditional stator shifted in phase by a partial pole position relativeto a phase of said first stator.
 21. The method in accordance with claim11, further including: truncating or padding the code to alter the codelength to match a predetermined number of poles in said stator.
 22. Themethod in accordance with claim 11, further including: driving saidfirst stator with a drive based on a weighted sum of two or more copiesof the code shifted with respect to one another to achieve rotorposition interpolation between discrete pole positions.